type 8 alligation & mixtures based ratio & proportion problems Section-Wise Topic Notes With Detailed Explanation And Example Questions
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The following question based on ratio & proportion topic of quantitative aptitude
(a) 15 litres
(b) 10 litres
(c) 4 litres
(d) 3 litres
The correct answers to the above question in:
Answer: (b)
In original mixture,
Alcohol = 4x litres
Water = 3x litres
On adding 5 litres of water,
${4x}/{3x + 5} = 4/5$
20x = 12x + 20
8x = 20
$x = 20/8 = 5/2$
Quantity of alcohol
= $4x = 4 × 5/2$ = 10 litres
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Read more alligation and mixtures problems Based Quantitative Aptitude Questions and Answers
Question : 1
Two alloys are both made up of copper and tin. The ratio of copper and tin in the first alloy is 1 : 3 and in the second alloy is 2 : 5. In what ratio should the two alloys be mixed to obtain a new alloy in which the ratio of tin and copper be 8 : 3 ?
a) 3 : 8
b) 5 : 11
c) 4 : 7
d) 3 : 5
Answer »Answer: (c)
By rule of alligation
Required ratio
= $1/77 : 1/44$ = 4 7
Question : 2
A container contains 60 kg of milk. From this container 6 kg of milk was taken out and replaced by water. This process was repeated further two times. The amount of milk left in the container is
a) 43.74 kg
b) 47.6 kg
c) 39.64 kg
d) 34.24 kg
Answer »Answer: (a)
Amount of milk left
= Initial amount ×
$(1-\text”Amount taken out in each operation”/\text”Initial amount”)^3$
= $60(1 - 6/60)^3$
= $60(1 - 1/10)^3$
= $60 × 9/10 × 9/10 × 9/10$
= 43.74 kg.
Question : 3
200 litres of a mixture contains milk and water in the ratio 17 : 3. After the addition of some more milk to it, the ratio of milk to water in the resulting mixture becomes 7 : 1. The quantity of milk added to it was
a) 60 litres
b) 80 litres
c) 40 litres
d) 20 litres
Answer »Answer: (c)
Let the quantity of additional milk added = x litres
In the mixture of 200 litres,
Quantity of milk
= $17/20 × 200$ = 170 litres
Quantity of water = 30 litres
According to the question,
${170 + x}/30 = 7/1$
170 + x = 210
x = 210 - 170 = 40 litres
Question : 4
A container contains two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off and the container is filled with B, the ratio of A and B becomes 1:1. How many litres of liquid A was in the container initially ?
a) 36$3/4$
b) 26$3/4$
c) 16$1/2$
d) 26
Answer »Answer: (a)
Let Liquid A = 7x litres
Liquid B = 5x litres
In 9 litres,
A = $7/12 × 9 = 21/4$ litres
B = $5/12 × 9 = 15/4$ litres
$7x - 21/4 = 5x - 15/4 + 9$
$2x = 21/4 - 15/4 + 9$
$2x = {21 - 15 + 36}/4 =42/4$
$x = 21/4$
Liquid A = $7 × 21/4$
= $147/4 = 36{3}/4$ litre
Question : 5
A can contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. Litres of liquid A contained by the can initially was
a) 21
b) 25
c) 20
d) 10
Answer »Answer: (a)
Let A = 7x litre, B = 5x litre
In 9 litres of mixture,
A = ${7x}/{12x} × 9 = 21/4$ litres
B = ${5x}/{12x} × 9 = 15/4$ litres
In new situation,
${7x - 21/4}/{5x - 15/4 + 9} = 7/9$
${28x - 21}/{20x - 15 + 36} = 7/9$
252x - 189 = 140x + 147
112x = 336
x = 3
Initial quantity of liquid A
= 7x = 7 × 3 = 21 litres
Question : 6
There are three containers of equal capacity. The ratio of Sulphuric acid to water in the first container is 3 : 2, that in the second container is 7 : 3 and in the third container it is 11 : 4. If all the liquids are mixed together, then the ratio of Sulphuric acid to water in the mixture will be :
a) 60 : 29
b) 59 : 29
c) 61 : 28
d) 61 : 29
Answer »Answer: (d)
In the new vessel, we have.
Sulphuric acid
= $3/5 + 7/10 + 11/15$
=${18 + 21 + 22}/30 = 61/30$
Water = $2/5 + 3/10 + 4/15$
= ${12 + 9 + 8}/30 = 29/30$
Sulphuric acid : Water
= $61/30 : 29/30$= 61 : 29
GET ratio & proportion PRACTICE TEST EXERCISES
type 1 basic concepts of ratio & proportion
type 2 age based ratio & proportion problems
type 3 addition subtraction product on ratio & proportion
type 4 income & expenditure based ratio & proportion problems
type 5 shares & partnership based ratio & proportion problems
type 6 fractions based ratio & proportion problems
type 7 finding sum difference product based ratio & proportion problems
type 8 alligation & mixtures based ratio & proportion problems
type 9 coins & rupees based ratio & proportion problems
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