Yak Mixture Together With Alligation Problems Alongside Short-Cut Methods

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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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