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Q.

Susan invested certain amount of money in two schemes A and B, which offer interest at the rate of 8 % per annum and 9 % per annum respectively. She received ₹ 1860 as annual interest. However, had she interchanged the amount of investment in the two schemes, she would have received ₹20 more as annual interest. How much money did she invest in each scheme?


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a

Amount invested by A is Rs.10000 and in B is Rs.10000.

b

Amount invested by A is Rs.13000 and in B is Rs.12000.

c

Amount invested by A is Rs.11000 and in B is Rs.22000.

d

Amount invested by A is Rs.12000 and in B is Rs.10000. 

answer is D.

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Detailed Solution

Given that the interest rates in A and B are 8% and 9%, respectively.
After interchanging the interest rates in A and B are 9% and 8%, respectively and the amount received is Rs. 20 more.
 We know that Simple Interest  I= P×R×T 100 .
I = simple interest, P = principal, R = rate of interest, T = time.
Amount received A = P / I.
Let us consider the amount invested in A be Rs. x and in B be Rs. y.
The interest rates in A and B are 8% and 9%, respectively.
⇒0.08x+0.09y=1860 ……(1)
After interchanging the interest rates in A and B are 9% and 8%, respectively and the amount received is Rs. 20 more.
⇒0.09x+0.08y=1880 ……(2)
Let us multiply equation (1) with 8.
⇒0.64x+0.72y=14880 ……(3)
Now, multiply equation (2) with 9.
⇒0.81x+0.72y=16920 ……(4)
Subtract equation (3) from (4).
0.81x+0.72y=16920 −0.64x−0.72y=14880   --------------------------------
0 .17x=2040 =>0.17.5=2040 ⇒ x = 12000
Substitute the value of ‘x’ in equation (1).
=>0.08 12000 +0.09y=1860 ⇒y=10000 Hence, amount invested A is Rs. 12000 and in B is Rs. 10000.
The correct option is (4).
 
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