Question

A sum of ₹ 700 is used to give seven cash prizes to students of a school for their overall academic performance. If each prize is ₹ 20 less than its preceding prize, then find the value of the highest prize.

• A. ₹160
• B. ₹140
• C. ₹120
• D. ₹100

Answer 1

The correct option is A ₹160

As each prize is ₹20 less then then its preceding prize, value of each prize form an AP with common dfference of -₹20.

Let the highest prize or the first prize be a.

common difference(d) = -₹20
no of prizes(n) = 7
sum of all prizes(s) = 700

Sum of first n terms of an AP,
$S=\frac{n}{2}(2a+(n-1\left)d\right)$

700 = $\frac{7}{2}(2a+(7-1)-20)$

$\Rightarrow$ 200 = 2a-120
$\Rightarrow$ 320 = 2a
$\Rightarrow$ a = ₹160

$\therefore$ First prize = ₹160

Hence each cash prize will be
₹160, ₹140, ₹120, ₹100, ₹80, ₹60 and ₹40 and the highest prize is ₹160.