The ratio of alcohol and water in to two glasses is 2 : 3 and 5 : 4

1.	The ratio of alcohol and water in to two glasses is 2 : 3 and 5 : 4 respectively. In what ratio should the liquid in both the glasses be mixed to obtain a new mixture containing alcohol and water in the ratio 1 : 1?1. 5 : 92. 9 : 73. 7 : 54. 9 : 11
Answer» Correct Answer - Option 1 : 5 : 9 Given: Ratio of alcohol and water in first glass = 2 : 3 Ratio of alcohol and water in second glass = 5 : 4 Ratio of alcohol and water in the final mixture = 1 : 1 Calculation: Let the ratio of amounts of liquid mixed from first glass and second glass to obtain the final mixture be p : q Amount of alcohol in final mixture = 2/5 × p + 5/9 × q ⇒ 2p/5 + 5q/9 Amount of water in final mixture = 3/5 × p + 4/9 × q ⇒ 3p/5 + 4q/9 Final ratio of alcohol and water in the final mixture = (2p/5 + 5q/9)/(3p/5 + 4q/9) ⇒ (2p/5 + 5q/9)/(3p/5 + 4q/9) = 1/1 ⇒ (2p/5 + 5q/9) = (3p/5 + 4q/9) ⇒ 5q/9 – 4q/9 = 3p/5 – 2p/5 ⇒ q/9 = p/5 ⇒ p/q = 5/9 ∴ The ratio will be 5 : 9

The ratio of alcohol and water in to two glasses is 2 : 3 and 5 : 4 respectively. In what ratio should the liquid in both the glasses be mixed to obtain a new mixture containing alcohol and water in the ratio 1 : 1?1. 5 : 92. 9 : 73. 7 : 54. 9 : 11

Answer» Correct Answer - Option 1 : 5 : 9

Given:

Ratio of alcohol and water in first glass = 2 : 3

Ratio of alcohol and water in second glass = 5 : 4

Ratio of alcohol and water in the final mixture = 1 : 1

Calculation:

Let the ratio of amounts of liquid mixed from first glass and second glass to obtain the final mixture be p : q

Amount of alcohol in final mixture = 2/5 × p + 5/9 × q

⇒ 2p/5 + 5q/9

Amount of water in final mixture = 3/5 × p + 4/9 × q

⇒ 3p/5 + 4q/9

Final ratio of alcohol and water in the final mixture = (2p/5 + 5q/9)/(3p/5 + 4q/9)

⇒ (2p/5 + 5q/9)/(3p/5 + 4q/9) = 1/1

⇒ (2p/5 + 5q/9) = (3p/5 + 4q/9)

⇒ 5q/9 – 4q/9 = 3p/5 – 2p/5

⇒ q/9 = p/5

⇒ p/q = 5/9

∴ The ratio will be 5 : 9