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All questions of Ratio & Proportion for UPSC CSE Exam
Can you explain the answer of this question below:According to the Boyle’s law, at a constant temperature, pressure of a definite mass of gas is inversely proportional to the volume. If the pressure is reduced by 20%, find the respective change in volume.
- A:
-33.33%
- B:
+25%
- C:
-25%
- D:
+33.33%
The answer is b.
According to the Boyle’s law, at a constant temperature, pressure of a definite mass of gas is inversely proportional to the volume. If the pressure is reduced by 20%, find the respective change in volume.
-33.33%
+25%
-25%
+33.33%
|
Ishan Chaudhary answered |
Point mutation involves- a)Change in single base pair
- b)Deletion
- c)Insertion
- d)Duplication
Correct answer is option 'A'. Can you explain this answer?
Point mutation involves
a)
Change in single base pair
b)
Deletion
c)
Insertion
d)
Duplication
|
Honey answered |
Yes. it involves point mutation as in sickle call anaemia.
Arun has a certain amount of money in the denomination of 1 rupee and 10 rupee notes . T he number of 1 rupee notes multiplied by the number of 10 rupee notes is equal to the total money (in rupees) that he has. What is the total number of ten rupee notes that he can have?- a)11
- b)13
- c)15
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
Arun has a certain amount of money in the denomination of 1 rupee and 10 rupee notes . T he number of 1 rupee notes multiplied by the number of 10 rupee notes is equal to the total money (in rupees) that he has. What is the total number of ten rupee notes that he can have?
a)
11
b)
13
c)
15
d)
None of these
|
Dhruv Verma answered |
Let x = no. of Re 1 notes and y = no. of Rs 10 notes So, xy = x+ 10y ⇒xy = x + 10y Now, go through options
Two-fifth of Anil’s salary is equal of Bhuvan’s salary and seven -ninth of Bhuvan’s salary is equal to Chandra’s salary. The sum of the salary of all of them is Rs 770. Which of the following is the salary of each?- a)300, 225, 250
- b)500, 425, 375
- c)450, 180, 140
- d)520, 610, 475
Correct answer is option 'C'. Can you explain this answer?
Two-fifth of Anil’s salary is equal of Bhuvan’s salary and seven -ninth of Bhuvan’s salary is equal to Chandra’s salary. The sum of the salary of all of them is Rs 770. Which of the following is the salary of each?
a)
300, 225, 250
b)
500, 425, 375
c)
450, 180, 140
d)
520, 610, 475
|
Anaya Patel answered |
A metal trader buys 2 kinds of silver foils, the ratio of their prices being 1:4. He sells the alloy at Rs 90 per kg so that he can make a profit of 20%. If the ratio of their quantities present in a alloy is 6:1 respectively, find the purchase price of the foil present in lesser quantity.
- a)Rs 52.5
- b)Rs 55
- c)Rs 47.5
- d)Rs 45
Correct answer is option 'A'. Can you explain this answer?
A metal trader buys 2 kinds of silver foils, the ratio of their prices being 1:4. He sells the alloy at Rs 90 per kg so that he can make a profit of 20%. If the ratio of their quantities present in a alloy is 6:1 respectively, find the purchase price of the foil present in lesser quantity.
a)
Rs 52.5
b)
Rs 55
c)
Rs 47.5
d)
Rs 45
|
Arya Roy answered |
CP = 75
In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?- a)50
- b)100
- c)150
- d)200
Correct answer is option 'C'. Can you explain this answer?
In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?
a)
50
b)
100
c)
150
d)
200
|
Gowri Chakraborty answered |
Let x is the number of 25 paisa coins then 2x and 3x will be for 10 and 5 paisa coins.
Now 30 rupees equal to 30*100 paisa now total paisa equal to x*25+2x*10+3x*5=3000.
60x = 3000.
x = 50.
Now number 5 paisa coin is 3x equal to 3*50 = 150.
A bag contains Rs 600 in the form of one rupee, 50 paise and 25 paise coins in the ratio of 3:4:12. Find the total number of 25 paise coins in the bag.- a)75
- b)200
- c)300
- d)900
Correct answer is option 'D'. Can you explain this answer?
A bag contains Rs 600 in the form of one rupee, 50 paise and 25 paise coins in the ratio of 3:4:12. Find the total number of 25 paise coins in the bag.
a)
75
b)
200
c)
300
d)
900
|
|
Alok Verma answered |
Let 3x,4x,12x are the coins of 1Rs,50-paise,25-paise coins
3x*1+4x*1/2+12x*1/4 = 600
3x+2x+3x =600
8x=600
x=75
25-paise coins=12*75=900
3x*1+4x*1/2+12x*1/4 = 600
3x+2x+3x =600
8x=600
x=75
25-paise coins=12*75=900
Anand and Bhavana have a few one rupee, 50 paise and 25 paise coins each. The total amount with each of them is Rs 5. The number of coins of two of the three types of coins that Anand has are equal and same is the case for the coins that Bhavana has. If Anand has the maximum possible total number of coins, then find the maximum possible total number of coins that Bhavana can have given that she has fewer coins than Anand.- a)16
- b)12
- c)10
- d)9
Correct answer is option 'B'. Can you explain this answer?
Anand and Bhavana have a few one rupee, 50 paise and 25 paise coins each. The total amount with each of them is Rs 5. The number of coins of two of the three types of coins that Anand has are equal and same is the case for the coins that Bhavana has. If Anand has the maximum possible total number of coins, then find the maximum possible total number of coins that Bhavana can have given that she has fewer coins than Anand.
a)
16
b)
12
c)
10
d)
9
|
Nandita Kaur answered |
Village-chief contribution = Rs 1.2 lakhs, so villagers’ contribution = Rs 1.2 lakhs Now, Go through the options.
Can you explain the answer of this question below:The difference between the two positive numbers is 10 and the ratio between them is 5:3. Find the product of the two numbers.
- A:
375
- B:
325
- C:
275
- D:
125
The answer is a.
The difference between the two positive numbers is 10 and the ratio between them is 5:3. Find the product of the two numbers.
375
325
275
125
|
Subham Basu answered |
Let the nos. be 5x and 3x. then, 5x - 3x = 10 2x = 10, x = 5 Required product = 5x x 3x = 5 x 5 x 3 x 5 = 375
An alloy of manganese, tin and bronze contains 90% bronze, 7% manganese and 3% tin. A second alloy of bronze and tin is melted with the first and the mixture contains 85% of bronze, 5% of manganese and 10% of tin. What is the percentage of bronze in the second alloy?- a)67.5%
- b)72.5%
- c)77.5%
- d)82.5%
Correct answer is 'B'. Can you explain this answer?
An alloy of manganese, tin and bronze contains 90% bronze, 7% manganese and 3% tin. A second alloy of bronze and tin is melted with the first and the mixture contains 85% of bronze, 5% of manganese and 10% of tin. What is the percentage of bronze in the second alloy?
a)
67.5%
b)
72.5%
c)
77.5%
d)
82.5%
|
Sameer Rane answered |
Say M and N are the total volumes of first and second alloys respectively.
Say C, Z and T represent Copper, Tin and Zinc percentages respectively in second alloy.
⇒ C + Z + T = 100 …… Eq.1
Amount of copper in the mixture = 0.90M + (C/100) x N = 0.85 x (M + N)
⇒ 0.05M = (0.85 – C/100) x N
⇒ C = 85 – 5 x (M/N) ….. Eq.2
Amount of Zinc in the mixture = 0.07M + (Z/100) x N = 0.05 x (M + N)
⇒ 0.02M = (0.05 – Z/100) x N
⇒ Z = 5 – 2 x (M/N) ….. Eq.3
Amount of copper in the mixture = 0.03M + (T/100) x N = 0.10 x (M + N)
⇒ –0.07M = (0.10 – T/100) x N
⇒ T = 10 + 7 x (M/N) …… Eq.4
Given Zinc percent in second alloy is Zero
⇒ Z = 0
Eq.3 ⇒ 0 = 5 – 2 x (M/N)
⇒ M/N = 5/2
Substitute M/N = 5/2 in Eq.4
⇒ T = 10 + 7 x (5/2) = 10 + 17.5 = 27.5%
∴ Tin in second alloy = 27.5%
The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?- a)3 : 3 : 10
- b)10 : 11 : 20
- c)23 : 33 : 60
- d)Cannot be determined
Correct answer is option 'C'. Can you explain this answer?
The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?
a)
3 : 3 : 10
b)
10 : 11 : 20
c)
23 : 33 : 60
d)
Cannot be determined
|
Kavya Saxena answered |
Gandhiji owns cows, some black and some white. He finds that 4 black cows and 3 white cows gave the same amount of milk in 5 days as 3 black cows and 5 white cows gave in 4 days. What is the ratio of milk given by a black cow in a day to that given by a white cow in a day?- a)8 : 5
- b)5 : 8
- c)3 : 5
- d)5 : 3
Correct answer is option 'B'. Can you explain this answer?
Gandhiji owns cows, some black and some white. He finds that 4 black cows and 3 white cows gave the same amount of milk in 5 days as 3 black cows and 5 white cows gave in 4 days. What is the ratio of milk given by a black cow in a day to that given by a white cow in a day?
a)
8 : 5
b)
5 : 8
c)
3 : 5
d)
5 : 3
|
Janhavi Nambiar answered |
Let 1 black cow gives x litres milk in 1 day and 1 white cow gives y litres milk in 1 day. Then 5(4.x + 3y) = 4(3x + 5y) ⇒ 20x + 15y = 12x + 20y
Can you explain the answer of this question below:Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is:
- A:
27
- B:
33
- C:
49
- D:
55
The answer is B.
Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is:
27
33
49
55
|
Sagar Sharma answered |
Given:
The ratio of two numbers is 3:5
After subtracting 9 from each number, the new ratio is 12:23
Let's assume the two numbers in the original ratio are 3x and 5x.
Ratio of the new numbers:
(3x-9) : (5x-9) = 12 : 23
Cross-multiplying, we get:
12(5x-9) = 23(3x-9)
Simplifying the equation:
60x - 108 = 69x - 207
-9x = -99
x = 11
Finding the smaller number:
Smaller number = 3x = 3 * 11 = 33
Therefore, the smaller number is 33, which corresponds to option 'B'.
The ratio of two numbers is 3:5
After subtracting 9 from each number, the new ratio is 12:23
Let's assume the two numbers in the original ratio are 3x and 5x.
Ratio of the new numbers:
(3x-9) : (5x-9) = 12 : 23
Cross-multiplying, we get:
12(5x-9) = 23(3x-9)
Simplifying the equation:
60x - 108 = 69x - 207
-9x = -99
x = 11
Finding the smaller number:
Smaller number = 3x = 3 * 11 = 33
Therefore, the smaller number is 33, which corresponds to option 'B'.
Can you explain the answer of this question below:A and B invest Rs 12,000 and Rs 16,000 respectively in a business. At the year-end, they share the profit in the ratio of 3:1. If A has invested his capital for the whole year, for how many months B has invested his capital?
- A:
4 months
- B:
3 months
- C:
6 months
- D:
8 months
The answer is b.
A and B invest Rs 12,000 and Rs 16,000 respectively in a business. At the year-end, they share the profit in the ratio of 3:1. If A has invested his capital for the whole year, for how many months B has invested his capital?
4 months
3 months
6 months
8 months
|
Saranya Kaur answered |
Let B invested for n months
n = 3
Bidhan is planning to buy a bike worth Rs 35,000, provided his brother agrees to lend him 3/2 times the money. Bidhan contributes and the financer provides 3 times the brother’s contribution. How much does Bidhan’s brother contribute?- a)5,000
- b)7,500
- c)10,000
- d)7,000
Correct answer is option 'B'. Can you explain this answer?
Bidhan is planning to buy a bike worth Rs 35,000, provided his brother agrees to lend him 3/2 times the money. Bidhan contributes and the financer provides 3 times the brother’s contribution. How much does Bidhan’s brother contribute?
a)
5,000
b)
7,500
c)
10,000
d)
7,000
|
|
Nikita Singh answered |
The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?- a)8 : 9
- b)17 : 18
- c)21 : 22
- d)Cannot be determined
Correct answer is option 'C'. Can you explain this answer?
The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?
a)
8 : 9
b)
17 : 18
c)
21 : 22
d)
Cannot be determined
|
|
Ravi Singh answered |
The sum of the ages of the 4 members of Sinha family is 140 years. 5 years ago the ages of the 4 members Nishu, Vicky, Mrs Sinha and Mr Sinha were in the ratio of 2 : 3 : 7 : 8 . After how many years would Nishu be as old as the present age of his mother?- a)10yrs
- b)17yrs
- c)30 yrs
- d)32 yrs
Correct answer is option 'C'. Can you explain this answer?
The sum of the ages of the 4 members of Sinha family is 140 years. 5 years ago the ages of the 4 members Nishu, Vicky, Mrs Sinha and Mr Sinha were in the ratio of 2 : 3 : 7 : 8 . After how many years would Nishu be as old as the present age of his mother?
a)
10yrs
b)
17yrs
c)
30 yrs
d)
32 yrs
|
Lavanya Menon answered |
In a garrison of 3600 men, the provisions were sufficient for 20 days at the rate of 1.5 kg per man per day. If x more men joined, the provisions would be sufficient for 12 days at the rate of 2 kg per man per day. Find x.- a)600
- b)800
- c)900
- d)720
Correct answer is option 'C'. Can you explain this answer?
In a garrison of 3600 men, the provisions were sufficient for 20 days at the rate of 1.5 kg per man per day. If x more men joined, the provisions would be sufficient for 12 days at the rate of 2 kg per man per day. Find x.
a)
600
b)
800
c)
900
d)
720
|
|
Rhea Reddy answered |
Let x be the number of new men joined the garrison,
The total quantity of food is = 3600(20) (1.5) kg ----------1
Now the available food will be consumed by (3600+x) men
(3600+x) (12) (2) kg --------------2
1 = 2
Solving both the equations
3600(20) (1.5) = (3600+x) (12) (2)
108000 = 86400 + 24x
21600 = 24x
X = 900
900 more men joined the garrison.
The total quantity of food is = 3600(20) (1.5) kg ----------1
Now the available food will be consumed by (3600+x) men
(3600+x) (12) (2) kg --------------2
1 = 2
Solving both the equations
3600(20) (1.5) = (3600+x) (12) (2)
108000 = 86400 + 24x
21600 = 24x
X = 900
900 more men joined the garrison.
Salaries of Ravi and Sumit are in the ratio 2 : 3. If the 'salary of each' one of them is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's present salary?
- a)Rs. 17,000
- b)Rs. 20,000
- c)Rs. 25,500
- d)Rs. 38,000
Correct answer is option 'D'. Can you explain this answer?
Salaries of Ravi and Sumit are in the ratio 2 : 3. If the 'salary of each' one of them is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's present salary?
a)
Rs. 17,000
b)
Rs. 20,000
c)
Rs. 25,500
d)
Rs. 38,000
|
|
Sameer Rane answered |
∴ Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38000.
In a fort there are 1600 soldiers fighting a battle against their enemy. On a particular day after their morning meal the balance provision inside the fort is only sufficient for 12 days at the rate of 1.2 kg per day. If by the evening 400 soldiers die then for how many days will the provision be sufficient for remaining men at the rate of 1.6 kg per day. (Assume soldiers eat either in morning or in evening).- a)10
- b)8
- c)18
- d)12
Correct answer is option 'D'. Can you explain this answer?
In a fort there are 1600 soldiers fighting a battle against their enemy. On a particular day after their morning meal the balance provision inside the fort is only sufficient for 12 days at the rate of 1.2 kg per day. If by the evening 400 soldiers die then for how many days will the provision be sufficient for remaining men at the rate of 1.6 kg per day. (Assume soldiers eat either in morning or in evening).
a)
10
b)
8
c)
18
d)
12
|
|
Aarav Sharma answered |
Given information:
- Number of soldiers in the fort = 1600
- Provision available for 1 day = 1.2 kg
- Soldiers die in the evening and the remaining soldiers eat 1.6 kg per day
Calculation:
Total provision available in the fort = 1600 x 1.2 x 12 = 23,040 kg
After 400 soldiers die, the remaining soldiers = 1600 - 400 = 1200
The provision required for 1 day by 1200 soldiers = 1.6 x 1200 = 1920 kg
The total provision available after 400 soldiers die = 23,040 - (400 x 1.2) = 22,560 kg
The number of days this provision will last for 1200 soldiers = 22,560 / 1920 = 11.75 days
Since soldiers eat either in the morning or in the evening, we need to round off the answer to the lower integer value, i.e. 11 days.
Therefore, the answer is option 'D' - 12 days.
- Number of soldiers in the fort = 1600
- Provision available for 1 day = 1.2 kg
- Soldiers die in the evening and the remaining soldiers eat 1.6 kg per day
Calculation:
Total provision available in the fort = 1600 x 1.2 x 12 = 23,040 kg
After 400 soldiers die, the remaining soldiers = 1600 - 400 = 1200
The provision required for 1 day by 1200 soldiers = 1.6 x 1200 = 1920 kg
The total provision available after 400 soldiers die = 23,040 - (400 x 1.2) = 22,560 kg
The number of days this provision will last for 1200 soldiers = 22,560 / 1920 = 11.75 days
Since soldiers eat either in the morning or in the evening, we need to round off the answer to the lower integer value, i.e. 11 days.
Therefore, the answer is option 'D' - 12 days.
The sum of four numbers is 253. The ratio of the first number to the second number is 2:3. The ratio of the second number to the third number is 5:6. The ratio of the third number to the fourth number is 8:9. What is the average of the second number and the third number?- a)72
- b)132
- c)60
- d)66
Correct answer is option 'D'. Can you explain this answer?
The sum of four numbers is 253. The ratio of the first number to the second number is 2:3. The ratio of the second number to the third number is 5:6. The ratio of the third number to the fourth number is 8:9. What is the average of the second number and the third number?
a)
72
b)
132
c)
60
d)
66
|
|
Anaya Patel answered |
Let the 1stno. A = X
2nd no.= B , 3rd no.= C , 4th no. = D
A: B =2:3
A/B = 2/3
x/B =2/3
B= 3x/2
B:C=5:6
(3x/2)/ C= 5/6
C=( 6×3x)/2×5= 9x/5
C= 9x/5
C:D= 8:9
9x/5/ D = 8/9
D= (9x×9)/8×5= 81x/40
D= 81x/40
A+B+C+D= 253. (GIVEN)
x+ 3x/2+9x/5+81x/40
Lcm = 40
(40x+ 60x+ 72x+81x)/40= 253
253x= 253×40
X= (253×40)/253= 40
Ist no.(A)= X= 40
2no.(B)= 3x/2=( 3 × 40)/2= 60
3rd no.(C)= 9x/5 = (9×40)/5= 72
4th no.(D)= 81x/40=( 81×40/)/40= 81
Average of numbers= sum of observations/ total no.of observations
Average of 2nd no. & 3rd no.= (60+72)/2= 132/2= 66
2nd no.= B , 3rd no.= C , 4th no. = D
A: B =2:3
A/B = 2/3
x/B =2/3
B= 3x/2
B:C=5:6
(3x/2)/ C= 5/6
C=( 6×3x)/2×5= 9x/5
C= 9x/5
C:D= 8:9
9x/5/ D = 8/9
D= (9x×9)/8×5= 81x/40
D= 81x/40
A+B+C+D= 253. (GIVEN)
x+ 3x/2+9x/5+81x/40
Lcm = 40
(40x+ 60x+ 72x+81x)/40= 253
253x= 253×40
X= (253×40)/253= 40
Ist no.(A)= X= 40
2no.(B)= 3x/2=( 3 × 40)/2= 60
3rd no.(C)= 9x/5 = (9×40)/5= 72
4th no.(D)= 81x/40=( 81×40/)/40= 81
Average of numbers= sum of observations/ total no.of observations
Average of 2nd no. & 3rd no.= (60+72)/2= 132/2= 66
Read the passage below and solve the questions based on it.
A book having pages between 4,000 and 5,000 is divided into four parts, each part being divided into chapters. The total number of pages in each of the four parts is the same. The ratio of the chapters across all the parts is 6:5:10:14. The number of chapters in the fourth part is 70
Q.What is the total number of pages in the book?
- a)4,000
- b)4,800
- c)4,200
- d)4,600
Correct answer is option 'C'. Can you explain this answer?
Read the passage below and solve the questions based on it.
A book having pages between 4,000 and 5,000 is divided into four parts, each part being divided into chapters. The total number of pages in each of the four parts is the same. The ratio of the chapters across all the parts is 6:5:10:14. The number of chapters in the fourth part is 70
A book having pages between 4,000 and 5,000 is divided into four parts, each part being divided into chapters. The total number of pages in each of the four parts is the same. The ratio of the chapters across all the parts is 6:5:10:14. The number of chapters in the fourth part is 70
Q.What is the total number of pages in the book?
a)
4,000
b)
4,800
c)
4,200
d)
4,600
|
|
Palak Yadav answered |
► According to question, A:B:C:D = 6:5:10:14
► Now in D there are 70 chapters
Therefore, A:B:C:D = 30:25:50:70 [ Multiplying Each by 5 ]
L.C.M of 30, 25, 50, 70 is 1050
So each part should have 1050 pages.
So total pages = 4 x 1050 = 4200 ans.
► Now in D there are 70 chapters
Therefore, A:B:C:D = 30:25:50:70 [ Multiplying Each by 5 ]
L.C.M of 30, 25, 50, 70 is 1050
So each part should have 1050 pages.
So total pages = 4 x 1050 = 4200 ans.
Three friends A, B and C started a venture with capitals in the ratio of 4:1:15. At the end of every quarter A halves his capital, while B doubles his capital and C leaves his capital untouched. This process is repeated till the end of the year. If at the end of the year B ’ s share of the profit is Rs 22,000, what is the total profit?
- a)Rs 88,000
- b)Rs 1,10,000
- c)Rs 2,25,000
- d)Rs 1,21,000
Correct answer is option 'D'. Can you explain this answer?
Three friends A, B and C started a venture with capitals in the ratio of 4:1:15. At the end of every quarter A halves his capital, while B doubles his capital and C leaves his capital untouched. This process is repeated till the end of the year. If at the end of the year B ’ s share of the profit is Rs 22,000, what is the total profit?
a)
Rs 88,000
b)
Rs 1,10,000
c)
Rs 2,25,000
d)
Rs 1,21,000
|
|
Aarav Sharma answered |
Given, ratio of capitals of A, B and C = 4:1:15
Let the initial capitals of A, B and C be 4x, x and 15x respectively.
At the end of the first quarter, their capitals become:
A's capital = 4x/2 = 2x
B's capital = x × 2 = 2x
C's capital = 15x
Their new capital ratio is 2:2:15
Let the new capitals of A, B and C be 2y, 2y and 15y respectively.
At the end of the second quarter, their capitals become:
A's capital = 2y/2 = y
B's capital = 2y × 2 = 4y
C's capital = 15y
Their new capital ratio is 1:4:15
Let the new capitals of A, B and C be z, 4z and 15z respectively.
At the end of the third quarter, their capitals become:
A's capital = z/2
B's capital = 4z × 2 = 8z
C's capital = 15z
Their new capital ratio is 1:8:15
Let the new capitals of A, B and C be m, 8m and 15m respectively.
At the end of the year, the total profit is divided among A, B and C in the ratio of their capitals.
B's share of profit = (8m/24) × Total profit = Rs 22,000
Total profit = (22,000 × 24)/8 = Rs 66,000
Therefore, the total profit is Rs 1,21,000 (option D).
Let the initial capitals of A, B and C be 4x, x and 15x respectively.
At the end of the first quarter, their capitals become:
A's capital = 4x/2 = 2x
B's capital = x × 2 = 2x
C's capital = 15x
Their new capital ratio is 2:2:15
Let the new capitals of A, B and C be 2y, 2y and 15y respectively.
At the end of the second quarter, their capitals become:
A's capital = 2y/2 = y
B's capital = 2y × 2 = 4y
C's capital = 15y
Their new capital ratio is 1:4:15
Let the new capitals of A, B and C be z, 4z and 15z respectively.
At the end of the third quarter, their capitals become:
A's capital = z/2
B's capital = 4z × 2 = 8z
C's capital = 15z
Their new capital ratio is 1:8:15
Let the new capitals of A, B and C be m, 8m and 15m respectively.
At the end of the year, the total profit is divided among A, B and C in the ratio of their capitals.
B's share of profit = (8m/24) × Total profit = Rs 22,000
Total profit = (22,000 × 24)/8 = Rs 66,000
Therefore, the total profit is Rs 1,21,000 (option D).
A man has 25 paise, 50 paise and 1 Rupee coins. There are 220 coins in all and the total amount is 160. If there are thrice as many 1 Rupee coins as there are 25 paise coins, then what is the number of 50 paise coins?- a)60
- b)80
- c)100
- d)120
Correct answer is option 'A'. Can you explain this answer?
A man has 25 paise, 50 paise and 1 Rupee coins. There are 220 coins in all and the total amount is 160. If there are thrice as many 1 Rupee coins as there are 25 paise coins, then what is the number of 50 paise coins?
a)
60
b)
80
c)
100
d)
120
|
|
Rajeev Kumar answered |
Given:
Total coin = 220
Total money = Rs. 160
There are thrice as many 1 Rupee coins as there are 25 paise coins.
Concept used:
Ratio method is used.
Calculation:
Let the 25 paise coins be 'x'
So, one rupees coins = 3x
50 paise coins = 220 – x – (3x) = 220 – (4x)
According to the questions,
3x + [(220 – 4x)/2] + x/4 =160
⇒ (12x + 440 – 8x + x)/4 = 160
⇒ 5x + 440 = 640
⇒ 5x = 200
⇒ x = 40
So, 50 paise coins = 220 – (4x) = 220 – (4 × 40) = 60
∴ The number of 50 paise coin is 60.
Can you explain the answer of this question below:Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarter of a minute, how often does the other turn in 8 seconds? (Assume equal size cogs and equi-spaced).
- A:
24
- B:
16
- C:
32
- D:
8
The answer is a.
Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarter of a minute, how often does the other turn in 8 seconds? (Assume equal size cogs and equi-spaced).
24
16
32
8
|
Dhruv Mehra answered |
Option(A) is correctLess Cogs ⇒ more turns and less time ⇒ less turns Cogs Time TurnsA 54 45 80B 32 8 ?Number of turns required= 80 x (54/32) x (8/45) = 24 times
The first, second and third class fares between two railway stations, Patna and Lucknow were 10:8:3 and the number of first, second and third class passengers between the two stations was is 3:4:10. If total sales of the ticket is Rs 16,100, find the money obtained by the sales of second class tickets.- a)Rs 5,250
- b)Rs 5,600
- c)Rs 6,400
- d)Rs 6,650
Correct answer is option 'B'. Can you explain this answer?
The first, second and third class fares between two railway stations, Patna and Lucknow were 10:8:3 and the number of first, second and third class passengers between the two stations was is 3:4:10. If total sales of the ticket is Rs 16,100, find the money obtained by the sales of second class tickets.
a)
Rs 5,250
b)
Rs 5,600
c)
Rs 6,400
d)
Rs 6,650
|
|
Saumya Sengupta answered |
Let the fare of 1st, 2nd and 3rd class be lOx, 8x, and 3x respectively and let the no. of passengers of 1st, 2nd and 3rd class be 3y, 4y and lOy respectively, then 30xy + 32xy + 30xy = 16100 ⇒ 92xy = 16100 Hence xy = 175
Required amount = 32xy = 32 x 175 = 5600
Four numbers in the ratio of 1:3:4:7 add up to give a sum of 75. Find the value of the biggest number.- a)42
- b)35
- c)49
- d)63
Correct answer is option 'B'. Can you explain this answer?
Four numbers in the ratio of 1:3:4:7 add up to give a sum of 75. Find the value of the biggest number.
a)
42
b)
35
c)
49
d)
63
|
|
Kavya Saxena answered |
Method to Solve :
Let 1:3:4:7 be 1x, 3x, 4x, 7x respectively.
1x + 3x + 4x + 7x =7515x = 75
x = 75/15
x = 5
So, 1x = 1*5 = 5
3x = 3*5 = 15
4x = 4*5 = 20
7x = 7*5 = 35
If t : u = 7 : 4, then what is the value of (7t + 4u) : (7t - 4u)?- a)44 : 23
- b)23 : 45
- c)65 : 33
- d)46 : 25
Correct answer is option 'C'. Can you explain this answer?
If t : u = 7 : 4, then what is the value of (7t + 4u) : (7t - 4u)?
a)
44 : 23
b)
23 : 45
c)
65 : 33
d)
46 : 25
|
Anirudh Joshi answered |
Understanding the Ratio
Given the ratio t : u = 7 : 4, we can express t and u in terms of a single variable. Let:
- t = 7x
- u = 4x
where x is a common multiplier.
Calculating 7t + 4u
Now, we substitute t and u into the expression 7t + 4u:
- 7t = 7(7x) = 49x
- 4u = 4(4x) = 16x
Now, adding these:
- 7t + 4u = 49x + 16x = 65x
Calculating 7t - 4u
Next, we compute 7t - 4u:
- 7t = 49x
- 4u = 16x
Now, subtracting these:
- 7t - 4u = 49x - 16x = 33x
Finding the Ratio
Now, we need to find the ratio of (7t + 4u) to (7t - 4u):
- (7t + 4u) : (7t - 4u) = 65x : 33x
The x cancels out, giving us:
- 65 : 33
Final Result
Thus, the value of (7t + 4u) : (7t - 4u) is 65 : 33, which corresponds to option 'C'.
Given the ratio t : u = 7 : 4, we can express t and u in terms of a single variable. Let:
- t = 7x
- u = 4x
where x is a common multiplier.
Calculating 7t + 4u
Now, we substitute t and u into the expression 7t + 4u:
- 7t = 7(7x) = 49x
- 4u = 4(4x) = 16x
Now, adding these:
- 7t + 4u = 49x + 16x = 65x
Calculating 7t - 4u
Next, we compute 7t - 4u:
- 7t = 49x
- 4u = 16x
Now, subtracting these:
- 7t - 4u = 49x - 16x = 33x
Finding the Ratio
Now, we need to find the ratio of (7t + 4u) to (7t - 4u):
- (7t + 4u) : (7t - 4u) = 65x : 33x
The x cancels out, giving us:
- 65 : 33
Final Result
Thus, the value of (7t + 4u) : (7t - 4u) is 65 : 33, which corresponds to option 'C'.
Read the passage below and solve the questions based on it.
There are certain number of apples, guavas and oranges in a basket. The number of each variety is more than one. The ratio of the number of apples to the number of guavas is equal to the ratio of the number of guavas lo the number of oranges.Q.If the total number of fruits is 61, then find the number of guavas.- a)16
- b)20
- c)25
- d)Cannot be determined
Correct answer is option 'B'. Can you explain this answer?
Read the passage below and solve the questions based on it.
There are certain number of apples, guavas and oranges in a basket. The number of each variety is more than one. The ratio of the number of apples to the number of guavas is equal to the ratio of the number of guavas lo the number of oranges.
There are certain number of apples, guavas and oranges in a basket. The number of each variety is more than one. The ratio of the number of apples to the number of guavas is equal to the ratio of the number of guavas lo the number of oranges.
Q.
If the total number of fruits is 61, then find the number of guavas.
a)
16
b)
20
c)
25
d)
Cannot be determined
|
|
Akanksha Datta answered |
Number of apples/Number of guavas = Number of guavas/Number of oranges (Number of guavas)2 = Number of apples x Number of oranges This gives us a hint that Number of apples x Number of oranges should be a prefect square.
Now start using the options.
Option (b) satisfies the relationship (16/20 = 20/25)
Now start using the options.
Option (b) satisfies the relationship (16/20 = 20/25)
A man has rs.480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?- a)100
- b)50
- c)78
- d)90
Correct answer is option 'D'. Can you explain this answer?
A man has rs.480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
a)
100
b)
50
c)
78
d)
90
|
|
Aisha Gupta answered |
Given that a man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal.
We are to find the total number of notes he has.
Let x represents the number of notes of each of the three denominations.
Then, according to the given information, we have
If 0.75 : x :: 5 : 8, then x is equal to:- a)1.12
- b)1.2
- c)1.25
- d)1.30
Correct answer is option 'B'. Can you explain this answer?
If 0.75 : x :: 5 : 8, then x is equal to:
a)
1.12
b)
1.2
c)
1.25
d)
1.30
|
|
Aarav Sharma answered |
(x * 5) = (0.75 *8)
X=6/5 = 1.20
A is proportional to B. B is inversely proportional to C. C is proportional to the square of D. D is directly proportional to the cube root of E. Assuming positive integers, if A increases then E- a)Increases
- b)Decreases
- c)Cannot say
- d)Could increase or decrease
Correct answer is option 'B'. Can you explain this answer?
A is proportional to B. B is inversely proportional to C. C is proportional to the square of D. D is directly proportional to the cube root of E. Assuming positive integers, if A increases then E
a)
Increases
b)
Decreases
c)
Cannot say
d)
Could increase or decrease
|
|
Akanksha Datta answered |
P works twice as fast as Q, whereas P and Q together can work three times as fast as R. If P, Q and R together work on a job, in what ratio should they share the earnings?- a)2:1:1
- b)4:2:1
- c)4:3:2
- d)4:2:3
Correct answer is option 'A'. Can you explain this answer?
P works twice as fast as Q, whereas P and Q together can work three times as fast as R. If P, Q and R together work on a job, in what ratio should they share the earnings?
a)
2:1:1
b)
4:2:1
c)
4:3:2
d)
4:2:3
|
|
Akanksha Datta answered |
If P is taking 3 days to do some work, then Q takes 6 days to do the same work. Now, both of them will take 2 days to complete the work. So, R takes 6 days to complete the same work.
Hence, earning should be distributed in the ratio of their efficiency, i.e., 2 : 1 : 1.
Hence, earning should be distributed in the ratio of their efficiency, i.e., 2 : 1 : 1.
Anil started a manufacturing unit with a certain amount of money. After a few months, Dheeraj became his partner, contributing three times of what Anil had contributed. At the end of the year, each was entitled to half the total profit. If Anil started the unit in January, then when did Dheeraj join as a partner?- a)August
- b)September
- c)July
- d)October
Correct answer is option 'B'. Can you explain this answer?
Anil started a manufacturing unit with a certain amount of money. After a few months, Dheeraj became his partner, contributing three times of what Anil had contributed. At the end of the year, each was entitled to half the total profit. If Anil started the unit in January, then when did Dheeraj join as a partner?
a)
August
b)
September
c)
July
d)
October
|
Shraddha Dasgupta answered |
Two numbers are in the ratio 2:5. If 6 is added to both, their ratio changes to 4:7. What is the larger number?- a)6
- b)12
- c)15
- d)21
Correct answer is option 'C'. Can you explain this answer?
Two numbers are in the ratio 2:5. If 6 is added to both, their ratio changes to 4:7. What is the larger number?
a)
6
b)
12
c)
15
d)
21
|
Mihir Mehta answered |
Understanding the Problem
We have two numbers in the ratio 2:5. Let's denote these numbers as:
- First Number = 2x
- Second Number = 5x
After adding 6 to both numbers, their ratio changes to 4:7.
Setting Up the Equation
When we add 6 to both numbers, we can express the new situation as:
- New First Number = 2x + 6
- New Second Number = 5x + 6
According to the problem, the new ratio is:
(2x + 6) / (5x + 6) = 4/7
Cross-Multiplying to Solve
To eliminate the fraction, we can cross-multiply:
7(2x + 6) = 4(5x + 6)
This simplifies to:
14x + 42 = 20x + 24
Rearranging the Equation
Next, we rearrange it to isolate x:
14x - 20x = 24 - 42
This gives us:
-6x = -18
Thus, we find:
x = 3
Finding the Numbers
Now that we have x, we can find the original numbers:
- First Number = 2x = 2(3) = 6
- Second Number = 5x = 5(3) = 15
Conclusion
The larger number is:
- 15
Thus, the correct answer is option 'C'.
We have two numbers in the ratio 2:5. Let's denote these numbers as:
- First Number = 2x
- Second Number = 5x
After adding 6 to both numbers, their ratio changes to 4:7.
Setting Up the Equation
When we add 6 to both numbers, we can express the new situation as:
- New First Number = 2x + 6
- New Second Number = 5x + 6
According to the problem, the new ratio is:
(2x + 6) / (5x + 6) = 4/7
Cross-Multiplying to Solve
To eliminate the fraction, we can cross-multiply:
7(2x + 6) = 4(5x + 6)
This simplifies to:
14x + 42 = 20x + 24
Rearranging the Equation
Next, we rearrange it to isolate x:
14x - 20x = 24 - 42
This gives us:
-6x = -18
Thus, we find:
x = 3
Finding the Numbers
Now that we have x, we can find the original numbers:
- First Number = 2x = 2(3) = 6
- Second Number = 5x = 5(3) = 15
Conclusion
The larger number is:
- 15
Thus, the correct answer is option 'C'.
A and B invested Rs 12,000 and Rs 18,000 respectively in a business for the whole year. At the year-end, there was a total profit of Rs 2,000. What is the share of A in the profit?- a)Rs 800
- b)Rs 1,200
- c)Rs 1,600
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
A and B invested Rs 12,000 and Rs 18,000 respectively in a business for the whole year. At the year-end, there was a total profit of Rs 2,000. What is the share of A in the profit?
a)
Rs 800
b)
Rs 1,200
c)
Rs 1,600
d)
None of these
|
Glance Learning Institute answered |
Correct Answer- Option A
A sum of money is to be distributed among A, B, C, and D in the proportion of 5:2:4:3. If C gets Rs.1000 more than D, what is B’s share?- a)Rs.500
- b)Rs.1000
- c)Rs.1500
- d)Rs.2000
Correct answer is option 'D'. Can you explain this answer?
A sum of money is to be distributed among A, B, C, and D in the proportion of 5:2:4:3. If C gets Rs.1000 more than D, what is B’s share?
a)
Rs.500
b)
Rs.1000
c)
Rs.1500
d)
Rs.2000
|
S.S Career Academy answered |
Let shares of A, B, C and D are 5x, 2x, 4x and 3x respectively
4x - 3x = 1000, x =1000
B’s share = 2x = 2000
In what ratio must be 40% acid solution and 70% acid solution mixed in order to get 50% acid solution?- a)1 : 2
- b)2 : 1
- c)1 : 3
- d)3 : 1
Correct answer is option 'B'. Can you explain this answer?
In what ratio must be 40% acid solution and 70% acid solution mixed in order to get 50% acid solution?
a)
1 : 2
b)
2 : 1
c)
1 : 3
d)
3 : 1
|
|
S.S Career Academy answered |
40% → 50% ← 70%
70 – 50 = 20
50 – 40 = 10
Ratio = 20:10 = 2:1
70 – 50 = 20
50 – 40 = 10
Ratio = 20:10 = 2:1
An amount of money was distributed among A, B and C in the ratio a:b:c. Consider the following statements:1. A gets the minimum share if a is less than (b - c)
2. C gets the minimum share if c is less than (a + b)
3. B gets maximum share if b is greater than (a + c)How many of the above statements are correct?- a)Only one
- b)Only Two
- c)All three
- d)None
Correct answer is option 'A'. Can you explain this answer?
An amount of money was distributed among A, B and C in the ratio a:b:c. Consider the following statements:
1. A gets the minimum share if a is less than (b - c)
2. C gets the minimum share if c is less than (a + b)
3. B gets maximum share if b is greater than (a + c)
2. C gets the minimum share if c is less than (a + b)
3. B gets maximum share if b is greater than (a + c)
How many of the above statements are correct?
a)
Only one
b)
Only Two
c)
All three
d)
None
|
Stuti Rane answered |
Understanding the Distribution Statements
In this scenario, A, B, and C receive shares based on the ratio a:b:c. To analyze the correctness of the given statements, we will evaluate each one:
Statement 1: A gets the minimum share if a is less than (b - c)
- This statement is incorrect. For A to have the minimum share, 'a' must be the smallest among a, b, and c. The condition (b - c) does not guarantee 'a' is the smallest, as the values of b and c can vary.
Statement 2: C gets the minimum share if c is less than (a + b)
- This statement is correct. If c is less than the sum of a and b, it implies that C's share is smaller than the combined shares of A and B, making C the one who receives the minimum share.
Statement 3: B gets the maximum share if b is greater than (a + c)
- This statement is incorrect. For B to have the maximum share, 'b' must be the largest among a, b, and c. The condition (a + c) does not ensure that 'b' is greater than both 'a' and 'c', as a and c can be larger individually.
Summary of Correctness
- Only Statement 2 is correct. Therefore, the total number of correct statements is one.
Conclusion
The correct answer is option 'A': Only one statement is correct.
In this scenario, A, B, and C receive shares based on the ratio a:b:c. To analyze the correctness of the given statements, we will evaluate each one:
Statement 1: A gets the minimum share if a is less than (b - c)
- This statement is incorrect. For A to have the minimum share, 'a' must be the smallest among a, b, and c. The condition (b - c) does not guarantee 'a' is the smallest, as the values of b and c can vary.
Statement 2: C gets the minimum share if c is less than (a + b)
- This statement is correct. If c is less than the sum of a and b, it implies that C's share is smaller than the combined shares of A and B, making C the one who receives the minimum share.
Statement 3: B gets the maximum share if b is greater than (a + c)
- This statement is incorrect. For B to have the maximum share, 'b' must be the largest among a, b, and c. The condition (a + c) does not ensure that 'b' is greater than both 'a' and 'c', as a and c can be larger individually.
Summary of Correctness
- Only Statement 2 is correct. Therefore, the total number of correct statements is one.
Conclusion
The correct answer is option 'A': Only one statement is correct.
Ajay started a business by investing Rs5000. After 3 years, Binoy joined by investing Rs3000 whereas Ajay withdrew 1/5th of his capital. At the end of 12 years, they received a profit of Rs 52,000. What is Ajay’s share of profit?- a)18,000
- b)24,000
- c)34,000
- d)36,000
Correct answer is option 'C'. Can you explain this answer?
Ajay started a business by investing Rs5000. After 3 years, Binoy joined by investing Rs3000 whereas Ajay withdrew 1/5th of his capital. At the end of 12 years, they received a profit of Rs 52,000. What is Ajay’s share of profit?
a)
18,000
b)
24,000
c)
34,000
d)
36,000
|
Upsc Rank Holders answered |
After 3 years, Ajay’s share is 5000 – 1000 = 4000
Ratio or profit 5000 × 3 + 4000 × 9 : 3000 × 9 = 51 : 27 = 17 : 9
Ajay’s share = 17/26 × 52,000 = 34,000
Ratio or profit 5000 × 3 + 4000 × 9 : 3000 × 9 = 51 : 27 = 17 : 9
Ajay’s share = 17/26 × 52,000 = 34,000
Chapter doubts & questions for Ratio & Proportion - CSAT Preparation 2025 is part of UPSC CSE exam preparation. The chapters have been prepared according to the UPSC CSE exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for UPSC CSE 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
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