A pot contains 81 litres of pure milk- 1-3 of the milk is replaced by the same amount of water- Again 13 of the mixture is replaced by that amount of water- The ratio of milk and water in the new mixture is-

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Standard VII

Mathematics

Estimation Using Percentages in Situations

A pot contain...

Question

A pot contains $81$ litres of pure milk. $\frac{1}{3}$ of the milk is replaced by the same amount of water. Again $\frac{1}{3}$ of the mixture is replaced by that amount of water. The ratio of milk and water in the new mixture is:

1 : 2

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1 : 1

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2 : 1

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4 : 5

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Solution

The correct option is D $4 : 5$
Initially, Milk = 81 litres and waterr = 0 litre Afte 1st operation,
Milk = $[81 - \frac{1}{3} \times 81] l i t r e s = (81 - 27) l i t r e s = 54$ litres
Water = $[0 + \frac{1}{3} \times 54] l i t r e s$ = $(54 - 18)$ litres $= 36$ litres
Water= $[27 - \frac{1}{3} \times 27] l i t r e s + [\frac{1}{3} \times 54 + \frac{1}{3} \times 27] l i t r e s$ = $(27 - 9)$ litres + $(18 + 9)$ litres $= 45$ litres
$∴$ Required ratio of milk and water in the new mixture $= 36 : 45 = 4 : 5$

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A pot contains 81 litres of pure milk. 13 of the milk is replaced by the same amount of water. Again 13 of the mixture is replaced by that amount of water. The ratio of milk and water in the new mixture is:

A pot contains $81$ litres of pure milk. $\frac{1}{3}$ of the milk is replaced by the same amount of water. Again $\frac{1}{3}$ of the mixture is replaced by that amount of water. The ratio of milk and water in the new mixture is: