A mixture is made by mixing alcohol and water in the ratio 9 ∶ 7. If ‘x’…

Sum of first ratio = 9 + 7 = 16

Quantity of alcohol in 80 litres of mixture = 9/16 × 80 = 45 litres

Quantity of water in 80 litres of mixture = 7/16 × 80 = 35 litres

When ‘x’ litres of alcohol and ‘3x’ litres of water is added,

Quantity of alcohol in new mixture = 45 + x

Quantity of water in new mixture = 35 + 3x

But, ratio of new mixture = 13 ∶ 14

⇒ (45 + x)/(35 + 3x) = 13/14

⇒ 14(45 + x) = 13(35 + 3x)

⇒ 630 + 14x = 455 + 39x

⇒ 39x – 14x = 630 – 455

⇒ x = 175/25 = 7

∴ Total quantity of new mixture = 45 + x + 35 + 3x = 80 + 4(7) = 80 + 28 = 108 litres