replaced with water. This operation is done once more. If the ratio of milk and water now is 5 : 4, find the volume of the original solution.
In this case we have to work on proportion of milk,
We know 12 litres are drawn out. But we do not know the original volume and hence the fraction removed is unknown. Both the initial and final proportion of milk is given. Thus,
(
)
= × 2
5 4 fraction left after removal 9 5
(
)
⇒ fraction left after removal2= 25 36 = 5 fraction left after removal
6, i.e. fraction removed is 1 6.
But we know that 12 litres is drawn out. So 12 litres must be 1
6
th
of the total volume. Thus, total volume = 6 × 12 = 72 litres.
Exercise
11. From a solution which has milk and water in the ration 3 : 2, 20% of the solution is removed and replaced with water. What will be the ratio of milk and water in the resultant solution?
a. 13 : 12 b. 12 : 13 c. 1 : 1 d. 1 : 2
12. From a solution which has milk and water in the ration 3 : 1, 10% of the solution is removed and replaced with milk. What will be the ratio of milk and water in the resultant solution?
a. 31 : 9 b. 9 : 31 c. 27 : 13 d. 13 : 27
13. How many litres should be removed out of 48 litres of solution of milk and water and be replaced with equal amount of water so that the proportion of milk drops from 80% to 75%.
a. 2 lts b. 3 lts c. 10 lts d. 15 lts
14. When 20% of a solution of milk and water is removed and replaced with water, the ratio of milk and water becomes 2 : 3. Find the ratio of milk and water in the original solution.
a. 1 : 2 b. 2 : 1 c. 1 : 1 d. 1 : 3
15. From a solution having milk and water in the ratio 2 : 3, 15 lts of solution is drawn out and replaced with water. This operation is done a total of thrice. If the ratio of milk and water now is 25 : 231, find the volume of original solution.
Assignment: Averages & Weighted Averages | 93
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Assignment - Averages & Weighted Averages
1. The average sales for the months January to March is 40, the average sales for the months March to June is 50 and the average of the months January to June is 45. Find the sales in the month of March.
(a) 30 (b) 40 (c) 45 (d) 50
2. A class teacher buys caps for boys and girls in his class. There are 20 boys and 10 girls in the class. A cap for a boy costs Rs. 15 and for a girl costs Rs. 30. But the teacher wants everyone to pay equally. How much does every student pay?
(a) 30 (b) 25 (c) 20 (d) 18
3. The average age of women at a tea party is 58. When three women leave early and two join after those three have left, the average age of the women becomes 60. What is the difference between the sum of the ages of the group of three who left and that of the group of two who joined?
(a) 30 (b) 28 (c) 14 (d) 15
4. Ramprasad wanted to find average of all the prime numbers between 10 and 20. But erroneously he used a number N instead of 19, because of which he got the average as 18. What is the value of N – 19?
(a) 31 (b) 12 (c) –12 (d) 3
5. Nawab Pataudi had an average of 63 runs in first 15 matches and after having a good batting streak in next two matches, he increased the average to 65. What is his average in the last two matches?
(a) 75 (b) 80 (c) 34 (d) 40
6. What is the difference between average of first 50 odd numbers and average of first 51 even numbers?
(a) 2 (b) 0 (c) 1 (d) 3
7. Among three numbers, the first is twice the second and second is twice the third. If the average of the reciprocals of the three numbers is 7/12, the numbers are:
(a) 16, 8, 4 (b) 20, 10, 5 (c) 24, 12, 6 (d) 4, 2, 1
8. When a student weighing 68 kgs joins a group of 8 students, the average of the group increases by 1.5 kgs. Find the average of the original group.
(a) 53 (b) 54.5 (c) 56 (d) 57.5
9. If a student weighing 70 kgs joins a group of n students, the average of the group increases by 1 kgs. If the new student weighed 55 kgs, the average of the group would have declined by 2 kgs. Find n.
(a) 3 (b) 4 (c) 5 (d) 6
10. Ten years ago, the average age of a couple was 27 years old. Today also the average age of the couple and their baby is 27 years old. Find the present age of the baby.
(a) 4 (b) 5 (c) 6 (d) 7
11. In what ratio should be rice worth Rs. 20/kg be mixed with rice worth Rs. 15/kg to get rice worth Rs. 16.50/kg
(a) 3 : 7 (b) 7 : 3 (c) 5 : 1 (d) 2 : 5
12. How many litres of solutions having 30% milk and 70% milk should be mixed so that we get 40 litres of 45% milk solution?
94 | Assignment: Averages & Weighted Averages
13. A solution contains A and B in ratio 3 : 4. A second solution contains A and B in ratio 2 : 3. If 14 ltrs of first solution are mixed with 15 ltrs of second solution, find the ratio of A and B in the final mixture.
(a) 5/7 (b) 17/29 (c) 12/17 (d) 8/5
14. An oil merchant bought some 1200 litres of oil. Part of the stock was sold at 5% loss and the remaining part at 7% profit. If he made an overall profit of 2%, how many litres of oil was sold at a loss?
(a) 700 (b) 500 (c) 600 (d) 800
15. Contents of three vessels having volumes in the ratio of 2 : 3 : 4 and having solutions with milk concentrations of 40%, 30% and 20% are mixed together in a fourth large vessel. Find the concentration of milk after the mixing.
(a) 30 % (b) 27.7 % (c) 27.2 % (d) 26.1 %
16. How many litres of water needs to be added to 25 litres of a solution having milk and water in the ratio 8 : 5, such that the resultant has milk and water in the ratio 5 : 8.
(a) 15 (b) 20 (c) 25 (d) 30
17. 12 litres of milk is added to 30 litres of solution having milk and water in the ratio 3 : 5. Find the ratio of milk and water after the addition.
(a) 22 : 25 (b) 34 : 25 (c) 9 : 25 (d) 31 : 25
18. A 50 kg alloy of tin and lead has 60% lead in it. Some extra tin is added to make the percentage of tin in the alloy equal to 60%. What is the total weight of the alloy now?
(a) 80 kg (b) 100 kg (c) 75 kg (d) 60 kg
19. A bartender replaces 10 ltrs of wine with water in a cask full of wine. He again takes out 10 ltrs of mixture and replaces it with water. Now the ratio of wine to water in the solution is 9 : 16. What is the volume of the cask?
(a) 40 ltrs (b) 25 ltrs (c) 15 ltrs (d) 30 ltrs
20. A jar containing a mixture of milk and water has 40% milk. A part of this solution is replaced by another mixture of milk and water having 19% milk. If now the mixture has 26% milk, what fraction of the jar was replaced?
Time Speed & Distance | 95
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