A sum of Rs.1890 has to be used to give 9 prizes to the customers of a super market for their overall academic purchases. If each prize is Rs.30 less than its preceding price, what is the least value of the price ?

Question

A sum of Rs.1890 has to be used to give 9 prizes to the customers of a super market for their overall academic purchases. If each prize is Rs.30 less than its preceding price, what is the least value of the price ?

A. 80

B. 85

C. 90

D. 95

Answer: C. 90

Solution:

Let the least value of the prize = Rs. x

Then the next value of the prize is x+30 , x+60, x+90, ….x+240.

Given total amount of cash prizes = Rs.1890

–> x + (x+30) + (x+60) + (x+90) + ….+ (x+240) = 1890

–> 9x + (30 + 60 + 90 + 120 + 150 + 180 + 210 + 240) = 1890

–> 9x + 30(1 + 2 + 3 + 4….+ 8) = 1890

–> 9x + 30(36) = 1890

–> 9x = 810 –> x=90

Hence the least value of the prize x=90