Question

In 40 litres mixture of glycerine and
water, the ratio of glycerine and
water is 3 : 1. The quantity of water
added in the mixture in order to
make this ratio 2:1 is:
a) 15 litres
b) 10 litres
c) 8 litres
d) 5 litres​

Answer 1

Answer:

(d) 5 litres is the answer

Answer 2

Answer:

Option (d) is the correct answer.

Step-by-step explanation:

Step 1 of 2

The quantity of mixture of the glycerine and the water = $40$ litres

The ratio of glycerine to water = $3:1$

So, the quantity of the glycerine = $30$ litres

And the quantity of the water = $10$ litres

Let the water to be added further be $x$ litres.

And given new ratio is $2:1$.

Then,

New ratio = $\frac{Quantity\ of\ gylcerine}{Quantity\ of\ water + x}$

⇒  $\frac{2}{1} =\frac{30}{10+x}$ . . . . . (1)

Step 2 of 2

(a) If $x=15$ litres. Then,

From equation (1),

⇒ $\frac{2}{1} \neq \frac{30}{10+15}$

⇒ $\frac{2}{1} \neq \frac{30}{25}$

⇒ $2\neq \frac{6}{5}$

Thus, option (a) is incorrect.

(b) If $x=10$ litres. Then,

From equation (1),

⇒ $\frac{2}{1} \neq \frac{30}{10+10}$

⇒ $\frac{2}{1} \neq \frac{30}{20}$

⇒ $2\neq \frac{3}{2}$

Thus, option (b) is incorrect.

(c) If $x=8$ litres. Then,

From equation (1),

⇒ $\frac{2}{1} \neq \frac{30}{10+8}$

⇒ $\frac{2}{1} \neq \frac{30}{18}$

⇒ $2\neq \frac{5}{3}$

Thus, option (c) is incorrect.

(d) If $x=5$ litres. Then,

From equation (1),

⇒ $\frac{2}{1} = \frac{30}{10+5}$

⇒ $\frac{2}{1} = \frac{30}{15}$

⇒ $2=2$

Thus, option (d) is correct.

#SPJ2