Question

Three dancers X, Y and Z danced on different number of songs. The number of songs on which Y danced is 16 more than the average of the number of songs on which X and Z danced. The ratio of the number of songs on which X and Y is 27 : 32. The number of songs on which Z danced is 79. Find the number of songs on which X danced.

1. 85
2. 90
3. 81
4. 92

Answer 1

Correct Answer - Option 3 : 81

Given:

The number of songs on which Y danced = 16 more than the average of the number of songs on which X and Z

The ratio of number of songs on which X and Y danced = 27 ∶ 32

The number of songs on which Z danced = 79

Formula:

If the ratio of A and B is a ∶ b, assume A = ak and B = bk where k is a constant.

Calculation:

Let number of songs on which X and Y danced be 27x and 32x

The number of songs on which Y danced = 16 more than the average of the number of songs on which X and Z

⇒ 32x = 16 + (27x + 79)/2

⇒ 64x – 27x = 32 + 79

⇒ 37x = 111

⇒ x = 3

The number of songs on which X danced = 27x

⇒ 27 × 3 = 81

∴ The number of songs on which X danced is 81.