The total monthly electricity bill for a house consists of the sum of two parts, one part is proportional to number of rooms and the other part is proportional to number of units consumed. Rs. 400 is the monthly electricity bill for a house with 8 rooms and consuming 240 units and Rs. 320 is the monthly electricity bill for a house with 6 rooms and consuming 200 units. What is the monthly electricity bill for a house with m rooms and consuming n units?
- ARs. (40m + n)
- BRs. (20m + n)
- CRs. (40m + n)/2
- DRs. (30m + n)/2
Explanation
Write the bill as a·(rooms) + b·(units). Then 8a + 240b = 400 and 6a + 200b = 320. Multiplying the first by 3 and the second by 4 and subtracting gives 80b = 80, so b = 1 (Re 1 per unit). Substituting back, 8a = 400 − 240 = 160, so a = 20 (Rs. 20 per room). Hence the bill for m rooms and n units is Rs. (20m + n). The answer is (B).