1. In what ratio must tea worth Rs. 60 per kg be mixed with tea
worth Rs. 65 a Kg such that by selling the mixture at Rs. 68.20 a Kg ,there can
be a gain 10%?
A. 3 : 2
B. 2 : 3
C. 4 : 3
D. 3 : 4
2. A container contains a mixture of two liquids P and Q in the
ratio 7 : 5. When 9 litres of mixture are drawn off and the container is filled
with Q, the ratio of P and Q becomes 7 : 9. How many litres of liquid P was
contained in the container initially?
A. 23
B. 21
C. 19
D. 17
3. A vessel is filled with liquid, 3 parts of which are water and
5 parts of syrup. How much of the mixture must be drawn off and replaced with
water so that the mixture may be half water and half syrup?
A. 1/3
B. 1/4
C. 1/5
D. 1/6
4. In what ratio must water be mixed with milk costing Rs.12 per
litre in order to get a mixture worth of Rs.8 per litre?
A. 1 : 3
B. 2 : 2
C. 1 : 2
D. 3 : 1
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. 1 : 2
B. 2 : 1
C. 3 : 1
D. 1 : 3
6. In what ratio must a grocer mix two varieties of pulses costing
Rs.15 and Rs. 20 per kg respectively to obtain a mixture worth Rs.16.50 per Kg?
A. 1 : 2
B. 2 : 1
C. 3 : 7
D. 7 : 3
7. A merchant has 1000 kg of sugar part of which he sells at 8%
profit and the rest at 18% profit. He gains 14% on the whole. The Quantity sold
at 18% profit is
A. 300
B. 400
C. 600
D. 500
8. A dishonest milkman sells his milk at cost price but he mixes
it with water and thereby gains 25%. What is the percentage of water in the
mixture?
A. 25%
B. 20%
C. 22%
D. 24%
9. In what ratio must water be mixed with milk to gain 50/3% on
selling the mixture at cost price?
A. 6 : 1
B. 1 : 6
C. 1 : 4
D. 4 : 1
10. In what ratio must rice at Rs.7.10 be mixed with rice at
Rs.9.20 so that the mixture may be worth Rs.8 per Kg?
A. 5 : 4
B. 2 : 1
C. 3 : 2
D. 4 : 3
1.( A)Explanation :Cost Price(CP) of 1 Kg mixture = Rs. 68.20
Profit = 10%
Cost Price(CP) of 1 Kg mixture= (100/(100+Profit%))×SP
=100(100+10)×68.20
=100/110×68.20=682/11
= Rs.62
By the rule of alligation:
CP of 1 kg tea of 1st kind CP of 1 kg tea of 2nd kind
60 65
Mean Price
62
65 - 62 = 3 62 - 60 = 2
Hence required ratio = 3 : 2
2.( B)Explanation :Let's initial quantity of P in the container be 7x
and initial quantity of Q in the container be 5x
Now 9 litres of mixture are drawn off from the container Quantity of P in 9 litres of the mixtures drawn off = 9×7/12=63/12 =21/4
Quantity of Q in 9 litres of the mixtures drawn off =9×5/12=45/12=15/4
Hence Quantity of P remains in the mixtures after 9 litres is drawn off =7-21/4
Quantity of Q remains in the mixtures after 9 litres is drawn off =5x-15/4
Since the container is filled with Q after 9 litres of mixture is drawn off,Quantity of Q in the mixtures =5x-15/4+9=5x+21/4
Given that the ratio of P and Q becomes 7 : 9
(7x-21/4) : (5x+21/4)=7:9
(7x-21/4)/(5x+21/4)=7/9
63x-(9×21/4)=35x+(7×21/4)
28x=(16×21/4)
x=(16×21)/(4×28)
litres of P contained in the container initially = 7x=(7×16×21)/(4×28)
=(16×21)/(4×4) =21
3.( C)Explanation :Let the quantity of the initial liquid in the vessel = 8 litre
and quantity of water in the initial liquid = 3 litre
andquantity of syrup in the initial liquid = 5 litre
Let x litre of the mixture is drawn off and replaced with waterQuantity of water in the new mixture = 3-3x/8+x
Quantity of syrup in the new mixture = 5-5x/8
Given that in the new mixture, quantity of water = quantity of syrup 3-3x/8+x = 5-5x/8
10x/8=2
5x/4=2
x=8/5 :8/5litre
Initially we assumed that the quantity of the initial liquid in the vessel = 8 litre for
the ease of calculations. For that 8/5 litre of the mixture to be drawn off and replaced with water so that the mixture may be half water and half syrup
Now, if the initial liquid in the vessel = 1 litre, quantity of the mixture to be drawn off and replaced with water so that the mixture may be half water and half syrup
=8/5×1/8=1/5
It means 1/5 of the mixture has to be drawn off and replaced with water so that the mixture may be half water and half syrup
4.(C)Explanation :By the rule of alligation, we have
Cost Price of 1 litre of water Cost Price of 1 litre of milk
0 12
Mean Price
8
12-8=4 8-0=8
Required Ratio = 4 : 8 = 1 : 2
5.(C)Explanation :By the rule of alligation, we have
Cost of 1 kg of 1st kind tea Cost of 1 kg tea of 2nd kind tea
62 72
Mean Price
64.5
72-64.5=7.5 64.5-62=2.5
Required Ratio = 7.5 : 2.5 = 3 : 1
6.(D)Explanation :By the rule of alligation,we have
CP of 1 kg of 1st variety pulse CP of 1 kg of 2nd variety pulse
15 20
Mean Price
16.5
20-16.5 = 3.5 16.5-15=1.5
Required Ratio = 3.5 : 1.5 = 35 : 15 = 7 : 3
7.(C)Explanation :By the rule of alligation,we have
Profit% by selling 1st part Profit% by selling 2nd part
8 18
Net % profit
14
18-14=4 14-8=6
=> Quantity of part1 : Quantity of part2 = 4 : 6 = 2 : 3
Total quantity is given as 1000Kg
So Quantity of part2 (Quantity sold at 18% profit) = 1000×3/5=600Kg
8.( B)Explanation :If a trader professes to sell his goods at cost price, but uses false weights, then Gain%=[Error/(True Value-Error)×100]%
Here Gain= 25%
Here error = quantity of water he mixes in the milk = x
Here the true value = true quantity of milk = T
So the formula becomes 25 = x/(T-x)×100
1 =x/(T-x)×4
T-x=4x
T= 5x
percentage of water in the mixture =x/T×100=x/5x×100=1/5×100=20%
9.(B).Explanation :Let CP of 1 litre milk = Rs.1
SP of 1 litre mixture = CP of 1 litre milk = Rs.1
Gain=50/3%
CP of 1 litre mixture = 100/(100+Gain%)×SP
=100/(100+50/3)×1=100/(350/3)=300/350=6/7
By the rule of alligation, we have
CP of 1 litre water CP of 1 litre milk
0 1
CP of 1 litre mixture
6/7
1 - 6/7 = 1/7 6/7 - 0 = 6/7
Quantity of water : Quantity of milk = 1/7 : 6/7 = 1 : 6
10.( D)Explanation :By the rule of alligation, we have
CP of 1 kg Rice of 1st kind CP of 1 kg Rice of 2nd kind
7.1 9.2
Mean Price
8
9.2 - 8 = 1.2 8 - 7.1 = .9
Required ratio = 1.2 : .9 = 12 : 9 = 4 : 3
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