Question

A sum of Rs.700 has to be used to give seven cash prizes to the students of a school for their overall academic performance. If each prize is Rs.20 less than its preceding prize, what is the least value of the prize?  

(a) Rs. 30 (b)Rs.40 (c) Rs. 60 (d) Rs. 80

Answer 1

(b) Let the least value be x. Then the next value is x + 20 and the next value is x + 40 and so on. 

According to question 

(x) + (x + 20) + (x + 40) + (x + 60) + (x + 80) + (x + 100) + (x + 120) = 700 

⇒ 7x + (20 + 40 + 60 + 80 + 100 + 120) = 700 

⇒7x + 20 (1 + 2 + 3 + 4 + 5 + 6) = 700 

⇒ 7x + 20 × 21 = 700 

⇒ 7(x + 60) = 7(100) 

⇒ x = 40