Mixture & Alligation
Question
Q1.
In what ratio should milk and water be mixed so that on selling at the cost price a profit of 10/3% is made ?
(a) 30 : 1 (b) 1 : 2 (c) 3 : 1 (d) 6 : 5
Solution.
milk : water = 100 : 10/3 = 300 : 10
= 30 : 1
Solution
Q2.
A merchant has 60 kg of rice, he sold x kg at 10% profit and the rest at 16% profit. He gain 12% on the whole . Find x .
(a) 40 kg (b) 30 kg (c) 10 kg (d) 32 kg
Solution.
=
Qty of 1st part/Qty of 2nd part
=
16 - 12/12 - 10
=
4/2
= 2 : 1
= 2/3 x 60
= 40 kg
Solution
Q3.
A farmer has 90 kg of rice , a part of which he sells at 15% profit and the rest at 5% loss. He earns 9% on the whole . What is the ratio
at which he sold both quantities .
(a) 4:3 (b) 7:3 (c) 10:3 (d) 2:5
Solution.
(b) 7:3
Solution
Q4.
A manager's expenditure and saving are in the ratio 7:15 . His income increases by 15%. His expenditure also increases by 30%, By how many
percent does her saving increases?
(a) 9% (b) 10% (c) 8% (d) 6%
Solution.
(c) 8%
Solution
Q5.
How many Kg of sugar at 38 per kg , must a man mix with 25 per kg , so that he may , on selling the mixture at 40 per kg gain 25% on the whole lot.
(a) 6 : 7 (b) 1 : 2 (c) 4 : 5 (d) 9 : 10
Solution.
CP of mixture = 40 x
100/125
= 40 x
4/5
= 32 per kg
Qty of cheaper/Qty of dearer
=
CP of dearer - mean P/Mean P - CP of cheaper
=
38 - 32/32 - 25
=
6/7
= 6 : 7
Solution
Q6.
In what proportion must water be mixed with milk to gain 50/3% by selling it at cost price ?
(a) 1 : 6 (b) 6 : 1
(c) 2 : 1 (d) 1 : 4
Solution.
(a) 1 : 6
Solution
Q7.
Milk and water are mixed in a vessel A in the proportion 5:3 and in vessel B in the proportion 6:5. In what proportion should quantities
be taken from the two vessels so as to form a mixture in which milk and water will be in the proportion of 7:5 ?
(a) 12 : 17 (b) 11 : 10 (c) 2 : 9 (d) 3 : 4
Solution.
(b) 11 : 10
Solution
Q8.
A person has a milk of Rs.30 per litre. In what ratio should water be mixed in this so that after selling the mixture at Rs.30 he may get a profit of 20% (milk is to water)
(a) 2:3 (b) 5:4 (c) 5:1 (d) 1:4
Solution.
(c) 5:1
Solution
Q9.
12kg of rice costing Rs. 30 per kg is mixed with 8 kg of rice costing Rs 40 per kg. The average per kg price of mixed rice is.
(a)Rs 38 (b)Rs37 (c)Rs35 (d)Rs34
Solution.
Total cost price of 20kg of mixed rice
Rs(12 x 30 + 8 x 40)
= Rs680
Average per kg price
680/20 = Rs34
Solution
Q10.
A some of Rs.41 was divided among 50 boys and girls each boys get 90 paise and each girl 65 paise . The number of girls will
be ____________ .
Solution.
In this case apply the alligation method , paise per students = (4100/50) = 82
boys: girls = (82 - 65) : (90 - 82)
Boys : girls = 17:8
number of girls = (50/25) x 8 = 16
Solution
