In an NCC camp, the average weight was 72 kg. If 5 cadets having average weight 76 kg leave and 11 cadets of average weight 79 kg join the group, the average weight of the cadets in the group increases by 0.6 kg. The number of cadets, initially in the group was:
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Correct answer: B
Explanation
The correct answer is option 2 i.e 89.
Let the initial number of cadets be x.
Initial total weight = 72 × x
Weight lost = 5 × 76 = 380
New total = 72x − 380
Weight added = 11 × 79 = 869
New total = 72x − 380 + 869 = 72x + 489
New number of cadets = x − 5 + 11 = x + 6
New average = (72x + 489) ÷ (x + 6) = 72 + 0.6 = 72.6
⇒ 72x + 489 = 72.6(x + 6)
⇒ 72x + 489 = 72.6x + 435.6
⇒ −0.6x + 489 = 435.6
⇒ −0.6x = 435.6 − 489 = −53.4
⇒ x = −53.4 ÷ −0.6 = 89