Question

An old lady Krishna Devi deposited ₹ 120000 in a bank at 8% interest p.a. She uses the annual interest to give five scholarships to the students of a school for their overall performances each year. The amount of each Scholarship is ₹ 300 less than the preceding scholarship. Find the amount of each scholarship. What values of lady are depicted here?

Answer 1

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.

HOPE THIS WILL HELP YOU...

Answer 2

P = 120000.
N = 1 year.
R = 8%.

Interest = PRN ÷ 100
= (120000 × 1 × 8 ) ÷ 100
= 960000 ÷ 100
= 9600

By given condition, scholarships are,
X ,X + 300, X + 600, X + 900, X + 1200.

By given condition,
Sum of scholarships = Interest.
X + X +300 + X + 600 + X + 900 + X + 1200 = 9600
5X + 3000 = 9600
5X = 9600 - 3000
5X = 6600
X = 1320

So, scholarships are 1320, 1620, 1920, 2220, 2520.

Hope it helps !! ;-)