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 7 rooms consuming 300 units?
- ARs. 500
- BRs. 440
- CRs. 340
- DRs. 300
Explanation
Let the bill be a rupees per room plus b rupees per unit, so bill = a·rooms + b·units. The data give 8a + 240b = 400 and 6a + 200b = 320. Halving and rearranging, 4a + 120b = 200 and 3a + 100b = 160, whose difference gives a + 20b = 40, so a = 40 − 20b. Substituting into 6a + 200b = 320 gives 240 − 120b + 200b = 320, hence b = 1 and a = 20. For 7 rooms and 300 units the bill is 7·20 + 300·1 = Rs. 440, option (B).