Question

A jar contains mixture of nilk and water in the ratio 3:4 respectively.24 litre of mixture is taken out and 24 litre of water is added to it .If the resultant ratio between milk and water is 2:1.What was the initial quantity of mixture in the jar?​

Answer 1

Answer: 84 litres

Given that a Jar contains mixture of milk and water in the ratio 3 : 4. respectively.

After taking out 24 litres of mixture from the jar and adding 24 litres of water. The ratio becomes 2 : 1.

Let the initial quantity of mixture in the jar be x litres. According to the question, ratio of milk and water is 3:4, Hence amount of milk and water in the jar are 3k litres & 4k litres respectively, Where k is a constant. Then,

⇒ Milk + Water = Mixture

⇒ 3k + 4k = x

⇒ 7k = x

⇒ k = x/7 ...(i)

Now, Adding 24 litres water and removing 24 litres of mixture from the Initial mixture, the ratio becomes 2 : 1 or the quantity of milk and water becomes 2k litres & k litre(s) respectively.

⇒ (Milk) + (Water + 24) = Initial Mixture - 24

⇒ (2k) + (1k + 24) = (x) - 24

⇒ 3k - x = -48

⇒ 3x/7 - x = -48 [ from (i), k = x/7 ]

⇒ (3x - 7x) / 7 = -48

⇒ -4x / 7 = -48

⇒ 4x/7 = 48

⇒ x = 48 × 7 / 4

⇒ x = 12 × 7

⇒ x = 84

Hence, The Initial mixture in the jar was of 84 litres.

Answer 2

Given :-

A  jar contains mixture of milk and water in the ratio 3:4 respectively.24 liter of mixture is taken out and 24 liter of water is added to it .If the resultant ratio between milk and water is 2:1.

To Find :-

What was the initial quantity of mixture in the jar?​

Solution :-

Let the ratio of milk and water be 4x and 3x.

Initial quantity be y

$\sf 3x + 4x = y$

$\sf 7x=y$

$\sf y = \dfrac{x}{7}(1)$

Now,

New ratio = 2:1

$\sf (2x) + (1x + 24) = y - 24$

$\sf 3x + 24 = \dfrac{y}{7} - 24$

$\sf 3x - y =0-48$

$\sf 3x-y=-48$

$\sf 3 \times \dfrac{y}{7} - y= -48$

$\sf\dfrac{3y}{7} - y = 48$

$\sf\dfrac{3y - 7(y)}{7} = -48$

$\sf \dfrac{-4y}7 = -48$

$\sf -4y = -48 \times 7$

$\sf -4y = -336$

$\sf 4y = 336$

$\sf y = \dfrac{336}{4}$

$\sf y = 84$