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QUESTION: 1

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?

Solution:

QUESTION: 2

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?

Solution:

QUESTION: 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?

Solution:

Let initially vessel have 8 l of liquid and x lof this liquid be replaced with water then quantity of water in new

QUESTION: 4

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?

Solution:

QUESTION: 5

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?

Solution:

QUESTION: 6

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%?

Solution:

The buying price is :

100/110 × 68.20 = 62

Let the amount of tea worth rs 60 be x and the amount of tea worth rs 65 be y

The total amount is : x + y

60x + 65y = 62(x + y)

60x + 65y = 62x + 62y

65y - 62y = 62x - 60x

3y = 2x

3/2 = x / y

3 : 2

QUESTION: 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

Solution:

Let the sugar sold at 8% gain = x

Therefore, Sugar sold at 18% gain = (1000 - x)

Let CP of sugar = Rs.y per kg

Total CP = Rs.100y

Therefore,

(108/100 * xy) + 118/100(1000-x)y

114/100*1000y

= 108xy + 118000y - 118xy = 114000y

10x = 4000

x = 400

Quantity sold at 18% profit

= 1000 - 400 = 600 kg

QUESTION: 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?

Solution:

Let C.P. of 1 litre milk be Re. 1

Then, S.P. of 1 litre of mixture = Re. 1, Gain = 25%.

C.P. of 1 litre mixture = Re.(100/125 * 1) = 4/5

By the rule of alligation, we have

Ratio of milk to water = 4/5 : 1/5

=> 4:5

Hence, percentage of water in the mixture = 1/5 x 100%

= 20%

QUESTION: 9

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?

Solution:

Let's assume cost of water is 0,

And the amount of water in mixture be x litres, and amount of milk in mixture be y litres,

So as per question the mixture would be sold a 8 Rs/litre

=> Cost of water per litre times amount of water in mixture of 1 litre + Cost of milk per litre times amount of milk in mixture of 1 litre must be equal to required cost of 1 litre mixture times 1 litre(total mixture quantity)

Mathematically, 0*x + 12*y = 8*1

=> 12 y = 8

=> y=2/3 litre

Now since total mixture is 1 litre,

So x = 1-y

x = 1-(2/3) = 1/3 litre

So ratio of water to milk in mixture, to get cost of required mixture to 1 litre = x/y = (1/3)/(2/3)

=> Ratio of water to milk in mixture is 1:2

QUESTION: 10

In what ratio must water be mixed with milk to gain 16 2/3 % on selling the mixture at cost price?

Solution:

Let C.P. of 1 litre milk be Rs. 1

S.P. of 1 litre of mixture = Rs. 1, Gain =

∴ C.P. of 1 litre of mixture =

BY the rule of alligation, we have:

∴ Ration of water and milk =

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