# In a 729 litres mixture of milk and water, the ratio of milk to water is 7 : 2. to get a new mixture containing milk and water in the ratio 7 : 3, the amount of water to be added is:

A. 81 litres

B. 71 litres

C. 56 litres

D. 50 litres

**Answer: Option A **

__Solution(By Examveda Team)__

Quantity of milk in 729 litre of mixture= 7 × $$\frac{{729}}{{9}}$$ = 567 litre

Quantity of water

= 729 - 567

= 162 litres

Let x litre of water be added to become ratio 7 : 3

Or, $$\frac{{7}}{{3}}$$ = $$\frac{{567}}{{162 + {\text{x}}}}$$

Or, 162 × 7 + 7x = 567 × 3

Or, 7x = 1701 - 1134 = 567

Or, x = $$\frac{{567}}{{7}}$$ = 81 litres water is to be added.

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Related Questions on Alligation

A. $$\frac{{1}}{{2}}$$ kg

B. $$\frac{{1}}{{8}}$$ kg

C. $$\frac{{3}}{{14}}$$ kg

D. $$\frac{{7}}{{9}}$$ kg

A. 81 litres

B. 71 litres

C. 56 litres

D. 50 litres

(Real/ratio)×added

={729/(7+2)}×(3-2)

=(729/9)×1

=81

7x+2x=9x

9x=729

2X=162

162+x/576=3/7

X=81

Milk : Water = 7 : 2

Milk : Water = 7 : 3

Now, (7 + 2) i.e 9 units ≡ 729 L

So, (3 - 2) i.e 1 units ≡ 81L (Ans.)

1st term 7:2 = 9

2nd term = 7:3 where only water difference 3-2 = 1

now

9x = 729

or x = 81

Qty of Milk = 729*(7/9) = 567 L

Qty of Water = 162 L

Had to mix water (3 - 2 ) = 1 unit

ATQ, 7 ≡ 567

Then, 1 ≡ (567/7) = 81 L

lets 1 part to be mixed so as per allegation method take only same qty ratio

so i am taking water ration

2/9 : 1(assume 1 part water to be mixed)

3/10

(1-3/10=7/10) (3/10-2/9= 7/90)

so ratio is 7/10 : 7/90 = 9:1

now water to be added 1/9 x729 = 81 litres

How about just taking 1 part of the ratio 7:2 which amounts to 81 litres. (1/9 of 729 = 81). Since 7:2 changes to 7:3. only 1 part of water is increasing.

Let 729=X

a:b = 7:2

c:d =7:3

formula : Water added=X(ad-bc)/c(a+b)

ans 81

if the raito was 7:2,then we r calculating as 7*729/2.Then as the same way for 7:3 we can calculate

Quantity of milk in 729 litre of mixture

7*729/10 =510.3

Quantity of water needed

729-510.3=218.7

As by 7:2 ratio the water was 162 litres.

Now by subtracting 162 from 218.7 ans comes

218.7-162=56.7

As the most appropriate ans is 56