Alligation & Mixtures Model Questions Set 1 Practice Questions Answers Test with Solutions & More Shortcuts

Question : 26

A trader has 50 kg of rice, a part of which he sells at 14% profit and the rest at 6% loss. On the whole his loss is 4%. What is the quantity sold at 14% profit and that at 6% loss?

a) 4, 46

b) 7, 43

c) 2, 48

d) 5, 45

e) None of these

Answer: (d)

Question : 27

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 in filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?

a) 20

b) 25

c) 10

d) 21

e) None of these

Question : 28

How many kg of salt at 42 P per kg must a man mix with 25 kg of salf at 24 P per kg so that he may, on selling the mixture at 40 P per kg gain 25% on the outlay?

a) 20

b) 30

c) 15

d) 25

e) None of these

Answer: (a)

Cost price of mixture = 40 × ${100}/{125}$P = 32P per kg

By the rule of fraction

Ratio = 4 : 5

Thus, for every 5 kg of salt at 24 P, 4 kg of salt at 42P is used.

∴ the required no. of kg = 25 × $4/5$ = 20.

Question : 29

Two vessels A and B contain spirit and water mixed in the ratio 5 : 2 and 7 : 6 respectively. Find the ratio in which these mixture be mixed to obtain a new mixture in vessel C containing spirit and water in the ratio 8 : 5 ?

a) 3 : 4

b) 7 : 9

c) 4 : 3

d) 5 : 6

e) None of these

Answer: (b)

Let the C.P. of spirit be Re. 1 per litre.

Spirit in 1 litre mix. of A = $5/7$ litre; C.p. of a litre mix. in A = Re. $5/7$ .

Spirit in 1 litre mix. of B = $7/{13}$ litre; C.P. of 1 litre mix. in

B = Re. $5/{13}$

Spirit in 1 litre mix. of C= $8/{13}$ litre; Mean price = Re. $8/{13}$

By the rule of alligation, we have :

∴ Required ratio = $1/{13}$ : $9/{13}$ = 7 : 9.

Question : 30

A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is:

a) $2/3$

b) $3/5$

c) $1/3$

d) $2/5$

e) None of these

Answer: (a)

By the rule of alligation, we have:

∴ So , Ratio of 1st and 2nd quantities = 7 : 14 = 1 : 2

∴ Required quantity replaced = $2/3$