The average monthly expenditure of a family was Rs. 2,500 during the first 4 months, Rs. 2,750 during the next 5 months and Rs. 3,550 during the last 3 months of a year. If the total saving during the year was Rs. 5,500, what was the average monthly income of the family?

Given:-

First 4 month average monthly expenditure of a family = 2,500 Rs.

Next 5 month average monthly expenditure of a family = 2,750 Rs.

Last 3 month average monthly expenditure of a family = 3,550 Rs.

Total saving of a family during a year = 5,500 Rs.

Concept Use :-

Average = \(\text{Sum} ~of ~all~ the ~quantity \over Total ~number ~of ~quantity\)

Income = Saving + Expenditure

Calculation :-

⇒ First 4 month total expenditure of a family = (First 4 month average monthly expenditure of a family ) × (Number of month)

⇒ First 4 month total expenditure of a family = (2500 Rs) ×( 4 ) = 10,000 Rs.

⇒ Next 5 month total expenditure of a family = (Next 5 month average monthly expenditure of a family) × (Number of month)

⇒ Next 5 month total expenditure of a family = (2750 Rs) × (5) = 13,750 Rs.

⇒ Last 3 month total expenditure of a family  = (Last 3 month average monthly expenditure of a family) × (Number of month)

⇒ Last 3 month total expenditure of a family = (3550 Rs) × (3) = 10,650 Rs.

Now,

⇒ Total Income of a family in a year = (Total saving of a family during a year ) + (First 4 month total expenditure of a family) + (  Next 5 month total expenditure of a family) + ( Last 3 month total expenditure of a family)

⇒ Total Income of a family in a year =  5,500 Rs + 10,000 Rs + 13,750 Rs + 10,650 Rs = 39,900 Rs.

⇒ Average monthly income of a family =  (Total Income of a family in a year) / (Total number of month in a year)

⇒ Average monthly income of a family = 39900/12 = 3325 Rs