Concept of “Average” [“औसत”]-05

Question: The average expenditure of a man for the first five months is Rs. 120 and for the next seven months is Rs. 130. His monthly average income if he saves Rs. 290 in that year, is  [एक व्यक्ति के पहले पांच महीनों के औसत खर्च 120 रूपये है तथा अगले सात महीनों का औसत खर्च 130 रूपये है. उस व्यक्ति की वार्षिक औसत आय बताइए, यदि उसने, उस वर्ष 290 रुपये बचाए हों.] [Ans. (c) Rs. 150]

(a) Rs.160  (b) Rs.170  (c) Rs. 150 (d) Rs.140 (e) none of these

Solution:

Detailed Explanation:

Concept: If all the items of any group are divided equally, then the equal value so obtained is said to be the average of the group.

First Method: In the given question, the average expenditure for the first five months is given Rs. 120 and the average expenditure for the next seven months is Rs. 130. If Rs. 10 × 5 = Rs. 50 is given to the expenditure for the first five months, then the average expenditure for the whole year becomes Rs. 130.

Now we have left Rs. 290 – Rs. 50 = Rs. 240 as saving [since the total saving for the whole year is given as Rs. 290]; which is to be distributed among 12 months, then each month will get Rs. 130 + Rs. 20 = Rs. 150. This is the average income for the whole year. Ans.

Second Method: Given that the average expenditure of a man for the first five months is Rs. 120 and for the next seven months is Rs. 130, so the total expenditure for the whole year = Rs. 120 ×5 + Rs. 130 × 7 = Rs. 600 + Rs. 910 = Rs. 1510

The saving for the whole year is given as Rs. 290.

Total income for the whole year = Rs. 1510 + Rs. 290 = Rs. 1800

Now, the average income for the whole year = Rs. 1800/12 = Rs. 150 Ans.