Question

A man invested 2/5 of his capital at 8% p.a., 3/8 of his capital at 10% p.a. and the remaining at 12% p.a. If his annual income at simple interest is rs 965 then his capital is -
Options-
A. Rs 8000
B. Rs 9000
C. Rs 10000
D. Rs 11000
(Question From IMO 2019-20 Q28)

Answer 1

If the man’s annual income at simple interest is rs 965 then his capital is option (c): Rs. 10,000

Step-by-step explanation:

Required formula:

S.I. = $\frac{P*R*T}{100}$

Let the capital invested by the man be denoted as “x”.

The man’s annual income at simple interest is given as Rs. 965

According to the question and based on to the above formula, we can write the equation as,

$\frac{\frac{2}{5} x * 8 * 1}{100} + \frac{\frac{3}{8}x * 10 * 1}{100} + \frac{(1- \frac{2}{5}-\frac{3}{8})x * 12 * 1}{100}$ = 965

⇒ $\frac{\frac{2}{5}x * 8}{100} + \frac{\frac{3}{8}x * 10}{100} + \frac{\frac{9}{40}x * 12}{100}$= 965

⇒ $\frac{16x}{5} + \frac{30x}{8} + \frac{108x}{40}$ = 965 * 100

⇒ $\frac{128x + 150x + 108x}{40}$ = 96500

⇒ 386x = 96500 * 40

⇒ x = $\frac{3860000}{386}$

⇒ x = Rs. 10,000

Thus, the capital invested by the man was Rs. 10,000.

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Answer 2

Answer:

The man’s net capital was rs 10000  (option C)

Step-by-step explanation:

Let the said capital be x  

Then 2/5 of x is invested at a simple interest rate of 8% p.a

3/8 of x is invested at the rate of  10% p.a

for us to obtain the remainder we add 2/5 to 3/8 that is,.

2/5x+3/8x = 31/40 x

Therefore the remainder is calculated from the whole which is 40/40

So 40/40x- 31/40x =9/40x

Therefore 9/40x is invested at the rate of 12% p.a  

The total simple interest earned  is rs 965 that year.

For us to obtain his capital , we will calculate for the sum of individual interest and then equate it to the total interest, that will be

(2/5x*8/100)+ (3/8x*10/100)+ (9/40x*12/100) =rs 965

0.032x +0.0375x +0.027x = rs 965

0.0965x = rs 965  

X=  rs 10000

Then the man’s net capital was rs 10000