Question

In a mixture, the ratio of milk and water is 8:7.if 11 litres of water is mixed in the ratio becomes 8: 9.Find the amount of milk in the initial mixture.

Answer 1

❍Let's consider the ratio of milk and water be 8x and 7x respectively.

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• As per given in the question In a mixture,the ratio of milk and water is 8:7.if 11 litres of water is mixed in the ratio becomes 8: 9.We are said to find the amount of milk in the mixture.

$\: \: \: \: \\ \\ \\ \: \: \: \sf \: : \implies \: \frac{8x}{7x + 11} = \frac{8}{9} \\ \\ \\ \: \: \: \sf \: : \implies \: 8x \times 9 = 8(7x + 11) \\ \\ \\ \: \: \: \sf \: : \implies \: 72x = 56x + 88 \\ \\ \\ \: \: \: \sf \: : \implies \: 72x - 56x = 88 \\ \\ \\ \: \: \: \sf \: : \implies \: 16x = 88 \\ \\ \\ \: \: \: \sf \: : \implies \: x = \frac{88}{16}$

$\large{\mathfrak{\underline{Substitute\:the\:values}}}$

$\: \: \: \\ \\ \sf \: the \: amount \: of \: milk = 8x \\ \\ \: \: \: \: \sf= 8 \times \frac{88}{16} \\ \\ \: \: \: \sf \: = 44 \: litres$

$\therefore$

Hence,the required amount of milk is 44 litres.

Answer 2

Step-by-step explanation:

In a mixture, the ratio of milk and water is 8:7.if 11 litres of water is mixed in the ratio becomes 8: 9.Find the amount of milk in the initial mixture.

Let the quantity of milk and water in the mixture are 2x and x respectively

After adding water in the mixture, the quantity of water in the mixture will be (x + 12)

According to question,

2x/(x + 12) = 4/3

⇒ 6x = 4(x + 12)

⇒ 6x = 4x + 48

⇒ 2x = 48

⇒ x = 24

So, the quantity of water in the new mixture = 24 + 12 = 36

∴ The quantity of water in the new mixture will be 36 litres