Yak Mixture Together With Alligation Problems Alongside Short-Cut Methods
P.S : Sorry for the bad handwriting :P
1. 729 liters of a mixture has milk in addition to H2O inward the ratio of 7:2. How much H2O should endure added to the mixture in addition to therefore that the ratio may instruct 7:3 ?
Solution :
2. In what proportion must tea at Rs. threescore per kg endure mixed tea at Rs. 88 per kg. So that the mixture may endure worth Rs. 68 kg ?
Solution :
Let X kg of tea at Rs. threescore per kg endure mixed amongst 1 kg of tea costing Rs. 88 kg.
So, Cost of X kg. of tea at Rs. threescore per kg. = Rs. threescore X
And toll of 1 kg of tea at Rs. 88 per kg. = Rs. 88
So, full toll of the mixture = Rs. (60 X + 88)
And the toll 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 H2O endure added to a liquid costing Rs. 12 per litre, in addition to therefore equally to brand a net turn a profit of 25% past times selling the diluted liquid at Rs. 13.75 per litre ?
Solution :
Shortcut Method :
4. How much H2O should endure added to twenty liter of milk at Rs. x equally liter in addition to therefore equally to convey a mixture worth Rs. 8 a liter ?
Solution :
Let the quantity of H2O to endure added endure X liters
Cost of twenty liters of milk at Rs. x a liter = twenty x x = 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 = v liters
5. Influenza A virus subtype H5N1 tea producer blends 2 qualities of tea from 2 dissimilar gardens, 1 costing Rs. 27 per kg in addition to the other Rs. xxx per kg inward the ratio v : 3. He sells the blended tea at Rs. 30.25 per kg. Find his percent net turn a profit ?
Solution :
Suppose he blended 5X kg tea of starting fourth dimension lineament in addition to 3X kg tea of minute quality
=> Cost of 5X kg of tea = 5X x 27 = Rs. 135 X
And the toll of 3X kg of tea = 3X x xxx = Rs. 90X
=> Cost of 8X kg of the mixed tea = 135X + 90X = Rs. 225X
in addition to 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 net turn a profit = (17X x 100) / 225X = 7(5/9) %
6. Two vessels comprise milk in addition to H2O respectively inward the ratio 3:1 in addition to 5:3. Find the ratio inward which these are to endure mixed to instruct a novel mixture inward which the ratio of milk to H2O is 2:1.
Solution :
In the starting fourth dimension vessel milk = 3/4 of the mixture
In the minute vessel milk = 5/8 of the mixture
It is required convey a mixture inward which milk is 2/3rd of novel mixture.
Let 1st mixture : sec mixture endure 1:X
So the book of resulting mixture = 1 + X
(milk inward the 1st mix.) + (milk inward the sec mix.) = (milk inward the resulting mix.)
So, these mixtures are to endure mixed inward 1:2
Shortcut Method :
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