# Quantitative Aptitude: Mixture and Alligation Set 15

1. A mixture contains milk and water in the ratio of 9 : 5. 14 liters of mixture is replaced by water, so that ratio of milk and water became 27 : 29. Find the quantity of initial mixture ?
40
56
38
42
70
Option B
Let quantity of milk and water = 9x and 5x
(9x – 14 * 9/14) / (5x-14 * 5/14 + 14) = 27/29
(9x – 9)/(5x + 9) = 27/29
261x – 261 = 135x + 243
x = 4
Initial quantity of mixture = 9x + 5x = 14x
= 14 * 4 = 56 liters

2. In a mixture quantity of milk and water 20 liters and 15 liters respectively. How much quantity of mixture will be replaced with water, so that ratio between milk to water became 12 : 23 ?
14
28
18
20
25
Option A
ratio of milk and water = 4 : 3
Let ‘X’ liters of mixture will be replaced with water.
(20-x * 4/7) / (15 – x * 4/7 + x) = 12/23
(20 – 4x/7) / (15 – 3x/7 + x) = 12/23
140 – 4x/105 + 4x = 12/23
x = 14

3. A solution contains lemon juice and water in the ratio of 4 : 1 . If 10 liter of solution is drawn and 15 liter of water is added, then ratio between juice to water become 2 : 3. Find the initial quantity of juice in the solution.
32 liters
14 liters
8 liters
20 liters
42 liters
Option D
Let quantity of juice and water in the solution 4x and x.
(4x – 8)/ (x – 2 + 15) = 2/3
4x – 8/ x + 13 = 2/3
x = 5
quantity of juice in the solution initially = 4x = 4 * 5 = 20 liters

4. Two alloys A and B contains iron and silver in ratio 4 : 3 and 9 : 5 equal quantity of both alloys are melted and recast into a new alloy what is the ratio between iron and silver in new alloy ?
17 : 11
5 : 9
3 : 2
4 : 5
15 : 14
Option A
quantity iron and silver in alloy A = 4/7 and 3/7 respectively.
quantity of iron and silver in alloy B = 9/14 and 5/14 respectively.
new ratio of iron and silver = (4/7 + 9/14) : (3/7 + 5/14)
= 17 : 11

5. In what ratio must two kinds of rice which cost rs.80 per kg and rs.92 per kg be mixed such that the resultant mixture cots rs.84 per kg ?
3 : 2
5 : 4
1 : 2
2 : 1
5 : 3
Option D
by allegation method,
80 92
84
8 4
2 : 1

6. A shopkeeper mixes two varieties of milk one costing at rs.20 per liter and the other at rs.28 per liter, then he sells the mixture at rs.36 per what ratio he mixed milk ?
2 : 3
5 : 4
2 : 1
9 : 2
CND
Option E
Here profit percentage is not given so we cant find the ratio.

7. A container contains 60 liters of a mixture of milk and water containing 60% milk. How many liters of water must be added to the container, so that quantity of milk is 40% of total mixture ?
40 liter
30 liter
40 liter
52 liter
54 liter
Option B
Total mixture = 60 liter
quantity of milk = 60 * 3/5 = 36
quantity of water = 60 * 2/5 = 24
now milk is 40% of total mixture,
total mixture = 36/40 * 100 = 90
quantity of water in new mixture = 90 – 36 = 54
extra liter water added = 54 – 24 = 30

8. A vessel contains 280 liters of mixture of milk and water and quantity of water is 40% of milk in the vessel. If 40 liters of water added in the vessel, then find the ratio of milk to water in resulting mixture ?
2 : 3
4 : 3
5 : 2
9 : 5
5 : 3
Option E
Ratio of milk and water = 100 : 40 = 5 : 2
quantity of milk = 280 * 5/7 = 200
quantity of water = 280 * 2/7 = 80
after adding 40 liter of water quantity of water = 80 + 40 = 120
new ratio = 200 : 120 = 5 : 3

9. In a 208 liter of mixture of milk and water the ratio of milk to water is 8 : 5. If ‘x’ liter of water is added in this mixture, so that the ratio of water to milk becomes 7 : 8. What is the value of ‘x’.
42 liter
32 liter
28 liter
30 liter
46 liter
Option B
quantity of milk = 208 * 8/13 = 128
quantity of water = 208 * 5/13 = 80
128/80 + x = 8/7
x = 32

10. A container contains 140 liter of mango juice. 40 liters are taken out of the vessel every day and an equal quantity of water is put in. Find how much mango juice is left in the vessel after 3 days ?
51.02 liter
32.12 liter
25 liter
46.25 liter
68.50 liter
Option A
using the formula
mango juice left over = (140 – 40/140)^3 * 140
= (100/140)^3 * 140
=125/343 * 140
= 51.02 liter