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P.S : Sorry for the bad handwriting :P
1. 729 liters of a mixture has milk and water in the ratio of 7:2. How much water should be added to the mixture so that the ratio may become 7:3 ?
Solution :
2. In what proportion must tea at Rs. 60 per kg be mixed tea at Rs. 88 per kg. So that the mixture may be worth Rs. 68 kg ?
Solution :
Let X kg of tea at Rs. 60 per kg be mixed with 1 kg of tea costing Rs. 88 kg.
So, Cost of X kg. of tea at Rs. 60 per kg. = Rs. 60 X
And cost of 1 kg of tea at Rs. 88 per kg. = Rs. 88
So, total cost of the mixture = Rs. (60 X + 88)
And the cost of (1+X) kg. at Rs. 68 per kg = (1+X) x 68
=> 60X + 88 = (1+X) x 68
=> 60X + 88 = 68 +68X
=> 68X - 68X = 88 - 68
=> 8X = 20
So, X = 20/8 = 5/2
So, the required ratio = 5:2
Shortcut Method :
3. In what ratio should water be added to a liquid costing Rs. 12 per litre, so as to make a profit of 25% by selling the diluted liquid at Rs. 13.75 per litre ?
Solution :
Shortcut Method :
4. How much water should be added to 20 liter of milk at Rs. 10 as liter so as to have a mixture worth Rs. 8 a liter ?
Solution :
Let the quantity of water to be added be X liters
Cost of 20 liters of milk at Rs. 10 a liter = 20 x 10 = Rs. 200
=> Quantity of the mixture = (20 + X) liters
=> Cost of mixture at Rs. 8 a liter = (20 + X) 8 = Rs (160 + 8X)
=> 160 + 8X = 200
=> 8X = 200 - 160 = 40
So, X = 40/8 = 5 liters
5. A tea producer blends two qualities of tea from two different gardens, one costing Rs. 27 per kg and the other Rs. 30 per kg in the ratio 5 : 3. He sells the blended tea at Rs. 30.25 per kg. Find his percentage profit ?
Solution :
Suppose he blended 5X kg tea of first quality and 3X kg tea of second quality
=> Cost of 5X kg of tea = 5X x 27 = Rs. 135 X
And the cost of 3X kg of tea = 3X x 30 = Rs. 90X
=> Cost of 8X kg of the mixed tea = 135X + 90X = Rs. 225X
and S.P of 8X kg of the mixed tea = 8X x 30.25 = Rs. 242X
=> Gain 8X kg of the mixed tea = 242X - 225X = Rs. 17X
=> Percent profit = (17X x 100) / 225X = 7(5/9) %
6. Two vessels contain milk and water respectively in the ratio 3:1 and 5:3. Find the ratio in which these are to be mixed to get a new mixture in which the ratio of milk to water is 2:1.
Solution :
In the first vessel milk = 3/4 of the mixture
In the second vessel milk = 5/8 of the mixture
It is required have a mixture in which milk is 2/3rd of new mixture.
Let 1st mixture : 2nd mixture be 1:X
So the volume of resulting mixture = 1 + X
(milk in the 1st mix.) + (milk in the 2nd mix.) = (milk in the resulting mix.)
So, these mixtures are to be mixed in 1:2
Shortcut Method :
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