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Important Questions Test: Ratio & Proportion- 2 - CAT MCQ


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15 Questions MCQ Test Quantitative Aptitude (Quant) - Important Questions Test: Ratio & Proportion- 2

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Important Questions Test: Ratio & Proportion- 2 - Question 1

What is the angle in degrees made by a sector, the ratio of whose area with the area of the semicircle is equal to 1:10?

Detailed Solution for Important Questions Test: Ratio & Proportion- 2 - Question 1

Area of semicircle = (1/2)πr2
Area of sector = (θ/360)πr2

Important Questions Test: Ratio & Proportion- 2 - Question 2

The value of a diamond varies directly as the square of its weight. If a diamond worth Rs 10,000 is divided into 2 pieces in the ratio of 4:6, what is the loss in value?

Detailed Solution for Important Questions Test: Ratio & Proportion- 2 - Question 2

V ∝ W2, V = KW2
Where, V = Value of diamond, W = weight of diamond and K = constant
⇒ 10000 = K.(10)2
⇒ K = 100
Hence, V = 100 x 42 = 1600
also, V = 100 x 62 = 3600
Net loss = Rs.(10000 - 5200) = Rs 4800 i.e., 48%

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Important Questions Test: Ratio & Proportion- 2 - Question 3

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.

Detailed Solution for Important Questions Test: Ratio & Proportion- 2 - Question 3

► Let the fare of 1st, 2nd and 3rd class be 10x, 8x, and 3x respectively.
► Let the no. of passengers of 1st, 2nd and 3rd class be 3y, 4y and 10y respectively. 
Then 30xy + 32xy + 30xy = 16100
⇒ 92xy = 16100
Hence xy = 175
Required amount = 32xy = 32 x 175 = 5600 

Important Questions Test: Ratio & Proportion- 2 - Question 4

Two horses cost as much as 5 dogs, 6 dogs as much as 8 oxen, 10 oxen as much as 50 sheep, 14 sheep as much as 9 goats. If the price of one goat is Rs 70, how much will one horse cost?

Detailed Solution for Important Questions Test: Ratio & Proportion- 2 - Question 4

► Price of one goat = Rs 70 ⇒ Price of 9 goats = 9 x 70 = Rs 630
► Price of 14 sheeps = Rs 630 
⇒ Price of 1 sheep = Rs 630/14 = Rs 45 ⇒ Price of 50 sheep = Rs 45 x 50 = Rs 2250
► Price of 10 oxen = 2250 ⇒ Price of 1 oxen = 225 ⇒ Price of 8 oxen  = 1800
► Price of 6 dogs = 1800 ⇒ Price of 1 dog = 300 ⇒ Price of 5 dog = 1500
► Price of two horses = 1500 ⇒ Price of one horse = 750

Important Questions Test: Ratio & Proportion- 2 - Question 5

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?

Detailed Solution for Important Questions Test: Ratio & Proportion- 2 - Question 5

► 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 = 253
    ⇒ (40x+ 60x+ 72x+81x)/40 = 253
    ⇒ 253x = 253*40
    ⇒ X = (253*40)/253 = 40
    ⇒ 1st no.(A) = X = 40
    ⇒ 2nd no.(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

Important Questions Test: Ratio & Proportion- 2 - Question 6

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 ?

Detailed Solution for Important Questions Test: Ratio & Proportion- 2 - Question 6

► 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
⇒ 1.x + 5.x + 10.x = 480
⇒ x + 5x + 10x = 480
⇒ 16x = 480
⇒ x = 30
► Therefore, the total number of notes is given by 
⇒ x + x + x = 3x = 3*30 = 90

Important Questions Test: Ratio & Proportion- 2 - Question 7

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?

Detailed Solution for Important Questions Test: Ratio & Proportion- 2 - Question 7

► Let A, B, C invested Rs 4x, Rs x, Rs 15x respectively.
► According to question, Ratio of their investments for 1 year
= (4x*3 + 2x*3 + x*3 + x/2*3) : (x*3 + 2x*3 + 4x*3 + 8x*3) : (15x*12)
⇒ 45x/2 : 45x : 180x
⇒ 45 : 90 : 360
⇒ 1 : 2 : 8
Total profit = (11/2)*22000 = Rs 121000

Important Questions Test: Ratio & Proportion- 2 - Question 8

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.

Detailed Solution for Important Questions Test: Ratio & Proportion- 2 - Question 8

CP = 75

Important Questions Test: Ratio & Proportion- 2 - Question 9

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?

Detailed Solution for Important Questions Test: Ratio & Proportion- 2 - Question 9

► 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.

Important Questions Test: Ratio & Proportion- 2 - Question 10

The ratio of the age of Sita and her mother is 2:3. N years from now, ratio of their ages will become 3:5. What is the value of N?

Detailed Solution for Important Questions Test: Ratio & Proportion- 2 - Question 10

► Let their present ages be 2x and 3x.
Given that

10x + 5N = 9x + 3N
X = -2N which 18 not possible.
Hence, correct option is (d).

Important Questions Test: Ratio & Proportion- 2 - Question 11

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 to the number of oranges.

Q.

If the total number of fruits is 61, then find the number of guavas.

Detailed Solution for Important Questions Test: Ratio & Proportion- 2 - Question 11

► 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)

Important Questions Test: Ratio & Proportion- 2 - Question 12

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?

Detailed Solution for Important Questions Test: Ratio & Proportion- 2 - Question 12

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.

Important Questions Test: Ratio & Proportion- 2 - Question 13

One part of a hostel’s monthly expenses is fixed, and the other part is proportional to the number of its boarders. The hostel collects ₹ 1600 per month from each boarder. When the number of boarders is 50, the profit of the hostel is ₹ 200 per boarder, and when the number of boarders is 75, the profit of the hostel is ₹ 250 per boarder. When the number of boarders is 80, the total profit of the hostel, in INR, will be 

Detailed Solution for Important Questions Test: Ratio & Proportion- 2 - Question 13

Total cost = Fixed cost + Variable cost

Variable cost = k × b
where, b = number of boarders and k = variable cost per boarder.

Total cost = FC + kb

Total collection = 1600b

Case 1: Total profit = 200 × 50 = 1600 × 50 – (FC + k × 50)   …(1)
Case 2: Total profit = 250 × 75 = 1600 × 75 – (FC + k × 75)   …(2)

(2) - (1), we get
18750 – 10000 = 1600 × 25 - 25k
⇒ k = 1250 and FC = 7,500 

Now, total profit when there are 80 boarders = 1600 × 80 – (7500 + 1250 × 80) = 20,500

Alternately,
Total cost when there are 50 students = (1600 – 200) × 50 = 70,000
Total cost when there are 75 students = (1600 – 250) × 75 = 1,01,250

Due to 25 students cost increases by (101250 - 70000) = 31250
∴ Due to 5 students cost increases by = 31250/5 = 6250

∴ Total cost when there are 80 students = 1,01,250 + 6250 = 1,07,500
Total revenue for 80 students = 1600 × 80 = 1,28,000

∴ Profit = 1,28,000 – 1,07,500 = 20,500.

Hence, option (d).

Important Questions Test: Ratio & Proportion- 2 - Question 14

In an examination, Rama's score was one-twelfth of the sum of the scores of Mohan and Anjali. After a review, the score of each of them increased by 6. The revised scores of Anjali, Mohan, and Rama were in the ratio 11 : 10 : 3. Then Anjali's score exceeded Rama's score by

Detailed Solution for Important Questions Test: Ratio & Proportion- 2 - Question 14

It is given that the scores of Anjali, Mohan and Rama after review were in the ratio 11 : 10 : 3

So, let their values be 11x, 10x and 3x respectively.

It is known that their score increased by 6 after review.

So, scores before review = 11x - 6, 10x - 6 and 3x - 6 respectively

Now, from the data given : (11x - 6 + 10x - 6) × 1/12 = 3x - 6

⇒ 21x - 12 = 36x - 72

⇒ 60 = 15x

⇒ x = 4

So, marks after revision are 44, 40 and 12 respectively.

Therefore, Anjali's score exceeded Rama's by 44 - 12 = 32 marks

Hence, option (b).

Important Questions Test: Ratio & Proportion- 2 - Question 15

Suppose, C1, C2, C3, C4, and C5 are five companies. The profits made by C1, C2, and C3 are in the ratio 9 : 10 : 8 while the profits made by C2, C4, and C5 are in the ratio 18 : 19 : 20. If C5 has made a profit of Rs 19 crore more than C1, then the total profit (in Rs) made by all five companies is:

Detailed Solution for Important Questions Test: Ratio & Proportion- 2 - Question 15


C5 – C1 = 19.
∴ 100x - 81x = 19
⇒ x = 1

∴ Total profit = 81x + 90x + 72x + 95x + 100x = 438x = 438 crore.

Hence, option (a).

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