Question

In a pot, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk, the pot would be full and ratio of milk and water would become 6 : 5. Find the capacity of the pot ?
A) 11 lit
B) 22 lit
C) 33 lit
D) 44 lit

Answer 1

Answer:

(D) :- 44 liters

Step-by-step explanation:

Please see below the explanation:

Let the capacity of the pot be 'P' litres.

Quantity of milk in the mixture before adding milk = 4/9 (P - 8)

After adding milk, quantity of milk in the mixture = 6/11 P.

So,

6P/11 - 8 = 4/9(P - 8)

10P = 792 - 352 => P = 44.

The capacity of the pot is 44 liters.

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Answer 2

Answer:

Step-by-step explanation:

Ratio:

• When comparing two quantities of the same type, ratio is used.
• The ratio formula for two numbers, a and b, is expressed as a: b or $\frac{a}{b}$

Given:

• Ratio of the mixture of milk and water  $= 4 : 5$

• After adding 8 liters of milk, the pot would be full and ratio of milk an ratio of the mixture of milk and water $= 6: 5$

To Find:

The capacity of the pot = ?

Solution:

Method 1:

Before adding the milk,

$M : W = 4 : 5$

After adding $8$ liters of milk,

$M : W = 6 : 5$

Here, $6$ units of Milk and $5$ units of water.

Difference in milk, after adding  $8$ liters of milk is

$M = 6 - 4 = 2 units$

so $8 liters = 2 units$, then $4 liters = 1 units$

The pot would be full at $11$ units(i.e. $6$ units of Milk and $5$ units of water.}

Capacity of Pot $= 11* 4$ liters

Capacity of Pot $= 44$ liters

So, the capacity of the pot is $44$ liters.

Method 2:

Let "C" be the capacity of the pot.

Before adding the milk,

$M : W = 4 : 5$

$M = \frac{4}{4+5} * (c - 8) = \frac{4}{9} * (c - 8)$

After adding $8$ liters of milk,

$M : W = 6 : 5$

$M = \frac{6}{6+5} * c = \frac{6}{11} * c$

By comparing ,

$\frac{6c}{11} - 8 = \frac{4}{9} * (c - 8)$

$\frac{6c}{11} - 8 = \frac{4c}{9} - \frac{4*8}{9}$

$\frac{6c}{11} - 8 = \frac{4c}{9} - \frac{32}{9}$

$\frac{6c}{11} -\frac{4c}{9} = 8 - \frac{32}{9}$

$\frac{(6c * 9) - (4c *11)}{11 * 9} = \frac{(8*9)-32}{9}$

$\frac{54c - 44c }{11 * 9} = \frac{72-32}{9}$

$\frac{10c }{11 * 9} = \frac{40}{9}$

$\frac{10c }{11 } = 40$

$10 c = 40 * 11$

$c = \frac{440}{10}$

$c = 44$

Therefore, the capacity of the pot is $44$ liters.

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