Question

. An old lady Krishna Devi deposited Rs. 12000 in a bank at 8% simple
interest p.a. She uses the annual interest to give five scholarships to thestudents of a school for their overall performances each year. The amountof each scholarship is 300 less than the preceding scholarship. Answerthe following(i) Find amount of each scholarship?(ii) What values of the lady are reflected?

Answer 1

Mistake in the question: amount deposited will be ₹120000 instead of ₹12000 .we can't give scholarship by ₹12000 for 5 students.

GIVEN:
Principal(P) = ₹ 120000
Rate (R)= 8%,
Time(T) = 1 year

S.I =( P x R x T)/100
= (120000 x 8 x 1) / 100 = ₹ 9600
Here, ₹9600 is to be used to give 5 scholarships.

Let the value of first scholarship be ₹ a, the value of second scholarship ₹ (a-300), the value of third scholarship [ (a-300)-300)] and so on.
Sn =₹ 9600, n = 5 , d= -300

Sn = n/2 [2a + (n-1) d

9600 = 5/2 [2×a +(5-1)×-300]
(9600 ×2)/5 = 2a + 4 ×-300
1920 ×2 = 2a - 1200
3840 + 1200 = 2a
5040 = 2a

a = 5040/2 = 2520

Hence, the value of first prize = ₹2520
the value of second prize = ₹2520 - ₹300 = ₹2200
the value of 3rd prize = ₹2200 - ₹300 = ₹1920
the value of 4th prize = ₹1920 - ₹300 = ₹1620
the value of 5th prize = ₹1620 - ₹300 = ₹1320.

The value of lady depicted here are love and charity.

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