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The average earning of a group of persons is Rs. 78 per day. The difference between the highest earning and lowest earning of any two persons of the group is Rs. 38. If these two people are excluded the average earning of the group decreases by Rs. 2. If the minimum earning of the person in the group lies between 67 and 73 and the number of persons in the group was equal to a prime number. The number of persons in the group initially was:1). 172). 193). 114). 13 |
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Answer» Let there be n people initially in the group ⇒ TOTAL earning of the group = n × 78 Let the highest earning be x + 38 and LOWEST earning be x ⇒ n × 78 = (n – 2) × 76 + (x + x + 38) ⇒ n × 78 = (n – 2) × 76 + (2x + 38) ⇒ 78n = 76n – 152 + 2x + 38 ⇒ 2n = 2x – 114 Given, ⇒ 66 < x < 71 n is prime number at x = 67 ⇒ 2n = 2 × 67 – 114 = 20 ⇒ n = 10 which is not a prime number at x = 68 ⇒ 2n = 2 × 68 – 114 = 22 ⇒ n = 11 which is a prime number ∴ Number of people in a group initially is 11 |
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