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All questions of Ratio, Proportion, Mixture and Partnership for SSC CGL Exam
A vessel contains 60 litres of milk. 12 litres of milk taken out from it and replaced by water. Then again from mixture, 12 litres are again taken out and replaced by water. The ratio of milk and water in the resultant mixture is: (SSC CHSL 1st Sit. 2015)- a)16 : 10
- b)9 : 5
- c)15 : 10
- d)16 : 9
Correct answer is option 'D'. Can you explain this answer?
A vessel contains 60 litres of milk. 12 litres of milk taken out from it and replaced by water. Then again from mixture, 12 litres are again taken out and replaced by water. The ratio of milk and water in the resultant mixture is: (SSC CHSL 1st Sit. 2015)
a)
16 : 10
b)
9 : 5
c)
15 : 10
d)
16 : 9
 | Ssc Cgl answered |
12l of milk taken out of 60l milk. So, 20% water is added to milk
Milk = 48l ; Water = 12l
Now, again 20% water is added to this mixture
So, ratio of milk and water = 38.4 : 21.6 = 16 : 9
Alternate Method:
Final Volume of milk = Initial volume
Milk = 48l ; Water = 12l
Now, again 20% water is added to this mixture
So, ratio of milk and water = 38.4 : 21.6 = 16 : 9
Alternate Method:
Final Volume of milk = Initial volume
A can is full of a mixture of a two liquids A and B in the ratio of 7 : 5. When 9 litres of mixture are drawn off from the can and replaced by the same quantity of liquid B, the ratio of A and B in the can becomes 7 : 9. The capacity of the can initially was (SSC Sub. Ins. 2016)- a)10 litres
- b)21 litres
- c)20 litres
- d)36 litres
Correct answer is option 'B'. Can you explain this answer?
A can is full of a mixture of a two liquids A and B in the ratio of 7 : 5. When 9 litres of mixture are drawn off from the can and replaced by the same quantity of liquid B, the ratio of A and B in the can becomes 7 : 9. The capacity of the can initially was (SSC Sub. Ins. 2016)
a)
10 litres
b)
21 litres
c)
20 litres
d)
36 litres
 | Malavika Rane answered |
Given data:
- Initial ratio of liquids A and B in the can = 7 : 5
- After drawing off and replacing with liquid B, the ratio becomes 7 : 9
Let's calculate the initial capacity of the can:
Let the capacity of the can be x litres.
Calculating the quantities of A and B initially:
- Quantity of A = 7x / (7+5) = 7x / 12
- Quantity of B = 5x / (7+5) = 5x / 12
Calculating quantities after the operation:
- Quantity of A after the operation = 7x / 12 - 9
- Quantity of B after the operation = 5x / 12 + 9
Given that the new ratio of A and B is 7 : 9:
- (7x / 12 - 9) / (5x / 12 + 9) = 7 / 9
- Solving the above equation, we get x = 21
Therefore, the initial capacity of the can was 21 litres.
- Initial ratio of liquids A and B in the can = 7 : 5
- After drawing off and replacing with liquid B, the ratio becomes 7 : 9
Let's calculate the initial capacity of the can:
Let the capacity of the can be x litres.
Calculating the quantities of A and B initially:
- Quantity of A = 7x / (7+5) = 7x / 12
- Quantity of B = 5x / (7+5) = 5x / 12
Calculating quantities after the operation:
- Quantity of A after the operation = 7x / 12 - 9
- Quantity of B after the operation = 5x / 12 + 9
Given that the new ratio of A and B is 7 : 9:
- (7x / 12 - 9) / (5x / 12 + 9) = 7 / 9
- Solving the above equation, we get x = 21
Therefore, the initial capacity of the can was 21 litres.
A milkman uses three containers for selling milk, their capacities being 40 L, 30 L and 20 L respectively. He fills respectively 87.5%, 80% and 90% of the containers with a mix of milk and water in the ratios, 3 : 2, : 5 : 1 and 7 : 2 respectively. What is the ratio of the total quantity of milk to that of water carried by him? (SSC CHSL-2018)- a)7 : 2
- b)31 : 12
- c)35 : 9
- d)5 : 2
Correct answer is option 'D'. Can you explain this answer?
A milkman uses three containers for selling milk, their capacities being 40 L, 30 L and 20 L respectively. He fills respectively 87.5%, 80% and 90% of the containers with a mix of milk and water in the ratios, 3 : 2, : 5 : 1 and 7 : 2 respectively. What is the ratio of the total quantity of milk to that of water carried by him? (SSC CHSL-2018)
a)
7 : 2
b)
31 : 12
c)
35 : 9
d)
5 : 2
 | EduRev SSC CGL answered |
Quantity in container of capacity
Quantity in container of capacity
Milk in three Containers
Ratio of milk to water
Quantity in container of capacity
Milk in three Containers
Ratio of milk to water
A box contain 280 coins of one rupee, 50 paise and 25 paise. The values of each kind of coin are in the ratio of 8 : 4 : 3. The number of one rupee coins will be (SSC Multitasking 2014)- a)52
- b)81
- c)60
- d)80
Correct answer is option 'D'. Can you explain this answer?
A box contain 280 coins of one rupee, 50 paise and 25 paise. The values of each kind of coin are in the ratio of 8 : 4 : 3. The number of one rupee coins will be (SSC Multitasking 2014)
a)
52
b)
81
c)
60
d)
80
 | Iq Funda answered |
Ratio of number of coins
= 8 : 4 × 2 : 3 × 4 = 8 : 8 : 12 = 2 : 2 : 3
= 8 : 4 × 2 : 3 × 4 = 8 : 8 : 12 = 2 : 2 : 3
Raman, Manan, and Kamal are partners and invest in a business such that Raman invests 2/5th of total and Manan invest 3/8th of the total. What is the ratio of profit of Raman, Manan and Kamal respectively? (SSC Sub. Ins. 2017)- a)16 : 15 : 9
- b)16 : 15 : 31
- c)2 : 3 : 5
- d)15 : 16 : 9
Correct answer is option 'A'. Can you explain this answer?
Raman, Manan, and Kamal are partners and invest in a business such that Raman invests 2/5th of total and Manan invest 3/8th of the total. What is the ratio of profit of Raman, Manan and Kamal respectively? (SSC Sub. Ins. 2017)
a)
16 : 15 : 9
b)
16 : 15 : 31
c)
2 : 3 : 5
d)
15 : 16 : 9
| | EduRev SSC CGL answered |
Let total investment = x
Investment by Raman = 2x / 5
Investment by Manan = 3x / 8
Investment by Kamal
Ratio of invest of Raman, Manan and Kamal
∴ Ratio of profit of Raman, Manan and Kamal
= 16 : 15 : 9
Investment by Raman = 2x / 5
Investment by Manan = 3x / 8
Investment by Kamal
Ratio of invest of Raman, Manan and Kamal
∴ Ratio of profit of Raman, Manan and Kamal
= 16 : 15 : 9
What is the ratio of the mean proportional between 8.1 and 3.6 and the third proportional of 2 and 3? (SSC Sub-Inspector-2018 )- a)5 : 6
- b)5 : 4
- c)6 : 5
- d)4 : 5
Correct answer is option 'C'. Can you explain this answer?
What is the ratio of the mean proportional between 8.1 and 3.6 and the third proportional of 2 and 3? (SSC Sub-Inspector-2018 )
a)
5 : 6
b)
5 : 4
c)
6 : 5
d)
4 : 5
| | Iq Funda answered |
Mean proportion of 8.1 and 3.6 = 11.7/2 = 5.8
and third proportion of 2 and 3 is = 3/0.66 = 4.5
and third proportion of 2 and 3 is = 3/0.66 = 4.5
If A and B are in the ratio 4 : 5 and the difference of their squares is 81, what is the value of A? (SSC CGL 1st Sit. 2015)- a)36
- b)15
- c)45
- d)12
Correct answer is option 'D'. Can you explain this answer?
If A and B are in the ratio 4 : 5 and the difference of their squares is 81, what is the value of A? (SSC CGL 1st Sit. 2015)
a)
36
b)
15
c)
45
d)
12
| | Iq Funda answered |
B2 - A2 = 81
Squaring both sides, we get
both sides subtract 1
Shortcut Method:
Let A be 4x and B be 5x
(5x)2 – (4x)2 = 81 (given)
9x2 = 81 ∴ x = 3
A = 3 × 4 = 12
Squaring both sides, we get
both sides subtract 1
Shortcut Method:
Let A be 4x and B be 5x
(5x)2 – (4x)2 = 81 (given)
9x2 = 81 ∴ x = 3
A = 3 × 4 = 12
A sum of ₹ 300 is divided among P, Q and R in such a way that Q gets ₹ 30 more than P and R gets ₹ 60 more than Q.
The ratio of their share is (SSC CGL 1st Sit. 2013)- a)3 : 2 : 5
- b)2 : 5 : 3
- c)5 : 3 : 2
- d)2 : 3 : 5
Correct answer is option 'D'. Can you explain this answer?
A sum of ₹ 300 is divided among P, Q and R in such a way that Q gets ₹ 30 more than P and R gets ₹ 60 more than Q.
The ratio of their share is (SSC CGL 1st Sit. 2013)
The ratio of their share is (SSC CGL 1st Sit. 2013)
a)
3 : 2 : 5
b)
2 : 5 : 3
c)
5 : 3 : 2
d)
2 : 3 : 5
 | Target Study Academy answered |
Q = P + 30 ⇒ Q – P = 30 and
R – Q = 60 = 2 × 30
∴ Required ratio = 2 : 3 : 5
Look : 3 – 2 = 1, 5 – 3 = 2
R – Q = 60 = 2 × 30
∴ Required ratio = 2 : 3 : 5
Look : 3 – 2 = 1, 5 – 3 = 2
A and B invest ₹ 3000 and ₹ 2400 respectively in a business. If, after one year, there is a loss of ₹ 720, how much loss will B bear? (Loss or Profit is in proportion to their investments) (SSC CGL 1st Sit. 2016)- a)₹ 72
- b)₹ 320
- c)₹ 400
- d)₹ 360
Correct answer is option 'B'. Can you explain this answer?
A and B invest ₹ 3000 and ₹ 2400 respectively in a business. If, after one year, there is a loss of ₹ 720, how much loss will B bear? (Loss or Profit is in proportion to their investments) (SSC CGL 1st Sit. 2016)
a)
₹ 72
b)
₹ 320
c)
₹ 400
d)
₹ 360
| | Snehal Patel answered |
Investment Overview
A and B have made investments in a business as follows:
- A invests: 3000
- B invests: 2400
Total Investment
The total investment in the business is:
- Total = 3000 + 2400 = 5400
Loss Distribution
There is a total loss of 720 after one year. This loss will be shared according to their investment ratios.
Investment Ratio
To find out how much loss each partner bears, we first calculate their investment ratios:
- Ratio of A's investment = 3000 / 5400
- Ratio of B's investment = 2400 / 5400
This simplifies to:
- A's ratio = 5/9
- B's ratio = 4/9
Calculating B's Loss
Now, we calculate B's share of the loss based on his investment ratio:
- B's loss = Total loss × B's ratio
- B's loss = 720 × (4/9)
To calculate B's loss:
- B's loss = 720 × 4 / 9
- B's loss = 720 × 0.4444 ≈ 320
Thus, B bears a loss of:
- 320
Conclusion
The correct answer is option 'B', which indicates that B will bear a loss of 320.
A and B have made investments in a business as follows:
- A invests: 3000
- B invests: 2400
Total Investment
The total investment in the business is:
- Total = 3000 + 2400 = 5400
Loss Distribution
There is a total loss of 720 after one year. This loss will be shared according to their investment ratios.
Investment Ratio
To find out how much loss each partner bears, we first calculate their investment ratios:
- Ratio of A's investment = 3000 / 5400
- Ratio of B's investment = 2400 / 5400
This simplifies to:
- A's ratio = 5/9
- B's ratio = 4/9
Calculating B's Loss
Now, we calculate B's share of the loss based on his investment ratio:
- B's loss = Total loss × B's ratio
- B's loss = 720 × (4/9)
To calculate B's loss:
- B's loss = 720 × 4 / 9
- B's loss = 720 × 0.4444 ≈ 320
Thus, B bears a loss of:
- 320
Conclusion
The correct answer is option 'B', which indicates that B will bear a loss of 320.
15 litres of a mixture contains alcohol and water in the ratio 1 : 4. If 3 litres of water is mixed in it, the percentage of alcohol in the new mixture will be (SSC CGL 2nd Sit. 2013)- a)15
- b)
- c)17
- d)
Correct answer is option 'B'. Can you explain this answer?
15 litres of a mixture contains alcohol and water in the ratio 1 : 4. If 3 litres of water is mixed in it, the percentage of alcohol in the new mixture will be (SSC CGL 2nd Sit. 2013)
a)
15
b)
c)
17
d)
 | Bayshore Academy answered |
Alcohol = 3 litres
Water = 12 litres
∴ Required percentage
Water = 12 litres
∴ Required percentage
Incomes of x and y are in the ratio 4 : 3. Their expenditures are in the ratio 12 : 7. Both save ₹ 3200 at the end of the month, then the income of x is: (SSC Sub. Ins. 2015)- a)₹ 6000
- b)₹ 8000
- c)₹ 2000
- d)₹ 4000
Correct answer is option 'B'. Can you explain this answer?
Incomes of x and y are in the ratio 4 : 3. Their expenditures are in the ratio 12 : 7. Both save ₹ 3200 at the end of the month, then the income of x is: (SSC Sub. Ins. 2015)
a)
₹ 6000
b)
₹ 8000
c)
₹ 2000
d)
₹ 4000
| | EduRev SSC CGL answered |
Ratio of income of x and y = 4 : 3
Ratio of expenditure of x and y = 12 : 7
Saving of x = 4a – 12b = 3200 ...(i)
Saving of y = 3a – 7b= 3200 ..(ii)
Solving (i) and (ii)
Now 3a = 3200 + 7b = 3200 + 7 (400) = 6000 a = ₹ 2000
So income of x = ₹ 2000 × 4 = 8000
Ratio of expenditure of x and y = 12 : 7
Saving of x = 4a – 12b = 3200 ...(i)
Saving of y = 3a – 7b= 3200 ..(ii)
Solving (i) and (ii)
Now 3a = 3200 + 7b = 3200 + 7 (400) = 6000 a = ₹ 2000
So income of x = ₹ 2000 × 4 = 8000
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