Question

A sum of Rs.1890 is to be used to give seven cash prizes.If each prize is Rs.50 less than the preceding prize,find the value of each prize?

Answer 1

Given,

Total number of cash prizes is $n=7$

Sum of all seven prizes is $S_7=1890Rs.$

and each price is $Rs.50$ less than preceding prize.

let, the first price be $a.$

The seven prizes are in a A.P given by:

$a,a-50,a-100,...\dots ,a-300$

Common difference of this A.P is $d=-50$

Sum of an A.P is given by:

$S_n=\frac{n}{2}(2a+(n-1\left)d\right)$

Hence,

$S_7=\frac{7}{2}(2a+(7-1\left)\right(-50\left)\right)$

$1890=\frac{7}{2}(2a-300)$

$1890=7a-1050$

$7a=1890+1050$

$7a=2940$

$a=\frac{2940}{7}$

$a=420$

Hence, value of seven cash prizes are:

$420,370,320,270,220,170,120$