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?
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 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?
Let initially vessel have 8 l of liquid and x lof this liquid be replaced with water then quantity of water in new
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?
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?
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%?
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
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
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(1000x)y
114/100*1000y
= 108xy + 118000y  118xy = 114000y
10x = 4000
x = 400
Quantity sold at 18% profit
= 1000  400 = 600 kg
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?
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%
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?
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 = 1y
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
In what ratio must water be mixed with milk to gain 16 2/3 % on selling the mixture at cost price?
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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