Average [औसत] -09 [SSC (GL), 2015 tier-1 ]

Question: The average weight of 15 oarsmen in a boat is increased by 1.6 kg, when one of the crew, who weighs 42 kg is replaced by a new man. Find the weight of the new man (in kg) [एक नौका में सवार 15  नाविकों का औसत वजन 1.6 किग्रा से बढ़ जाता है; जब 42 किग्रा के एक व्यक्ति की जगह एक नया व्यक्ति नाव पर आ जाता है. नए नाविक का वजन क्या है? (किग्रा में) [Ans. (b) 66]              

(a) 65        (b) 66       (c) 43       (d) 67

Solution:

Detailed Explanation: Concept: "When items of a group are equally distributed, then each value becomes equal. That each equal value is said to be “Average”.  When any value of the group is removed and a new value added; then if new value is equal to the removed value, then average is not affected. But, it the new value is more than the removed value, then average increases. If the new value is less than the removed value, then average decreases.

By substitution, if the average of the group increases or decreases, then the net change is added or subtracted respectively".  

Total increase in weight = 15 × 1.6 = 24

Weight of new person = 42 + 24 = 66 Ans.