Alligation & Mixtures Model Questions Set 1 Section-Wise Topic Notes With Detailed Explanation And Example Questions

Question : 1

A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is ___________.

a) 15%

b) 25%

c) 10%

d) 20%

e) None of these

Answer: (b)

We will apply alligaton on % profit. If he sells the milk at CP,

he gains 0%. But if he sells water at CP, he gains 100%.

Ratio of milk to water in the mixture should be 3 : 1

∴ % of water in mixture = $1/{3 + 1}$ × 100 = 25%

Question : 2

A can contains a mixture of two liquids A and B in proportion 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the proportion of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?

a) 21 l

b) 36 l

c) 20 l

d) 30 l

e) None of these

Answer: (b)

Apply alligation on fraction of A in each mixture.

Ratio of original mixture to B = $7/{16} : 7/{48}$ = 3 : 1

When 9 litres of B is mixed, original mixture should be $9/1$ × 3

= 27 litres.

Therefore initial quantity in can = 27 + 9 = 36 litres.

Question : 3

There are 65 students in a class. 39 rupees are distributed among them so that each boy gets 80 P and each girl gets 30 P. Find the number of boys and girls in that class.

a) 40, 25

b) 29, 36

c) 45, 20

d) 39, 26

e) None of these

Answer: (d)

Here, allegation is applicable for 'money per boy or girl".

Mean value of money per student = ${3900}/{65}$ = 60P

∴ Boys : Girls = 3 : 2

∴ Number of boys = ${65}/{3 + 2}$ × 3 = 39

and number of girls = 65 – 39 = 26

Question : 4

Jayashree purchased 150 kg of wheat of the rate of Rs. 7 per kg. She sold 50 kg at a profit of 10%. At what rate per kg should she sell the remaining to get a profit of 20% on the total deal?

a) 8.75

b) 9.75

c) 6.50

d) 7.50

e) None of these

Question : 5

In what ratio must tea at Rs. 62 per kg be mixed with tea at Rs. 72 per kg so that the mixture must be worth Rs. 64.50 per kg?

a) 3 : 2

b) 5 : 3

c) 3 : 1

d) 4 : 3

e) None of these

Answer: (c)

By the rule of alligation:

∴ Required ratio = 750 : 250 = 3 : 1.

Question : 6

A container contained 80 kg of milk. From this container, 8 kg of milk was taken out and replaced by water. This process was further repeated two times. How much milk is now contained by the container?

a) 56 kg

b) 59.46 kg

c) 48 kg

d) 58.32 kg

e) None of these