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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. 852. 903. 814. 92 |
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Answer» 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. |
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