Question

A sum of Rs. 1000 was lent to two people, one at the rate of 5 % and other at the rate of 8 %. If the simple interest after one year is Rs. 62, find the sum lent at each rate. (A) 700, 900 (B) 800, 1200 (C) 300, 500 (D) 400, 600

Answer 1

(D) 400, 600

The required sums are Rs. 400 and Rs. 600.

Step-by-step explanation:

Step 1.

Let the two amounts be x and (1000 - x).

Step 2.

Here, amount = x

time = 1 year

rate of simple interest = 5% p.a.

∴ interest = $\dfrac{x\times 1\times 5}{100}$

Step 3.

Here, amount = 1000 - x

time = 1 year

rate of simple interest = 8% p.a.

∴ interest = $\dfrac{(1000-x)\times 1\times 8}{100}$

Step 4.

According to the question,

$\dfrac{x\times 1\times 5}{100}+\dfrac{(1000-x)\times 1\times 8}{100}=62$

$\Rightarrow \dfrac{x}{20}+\dfrac{2000-2x}{25}=62$

$\Rightarrow \dfrac{5x+8000-8x}{100}=62$

⇒ 8000 - 3x = 6200

⇒ 3x = 1800

⇒ x = 600

Then, 1000 - x = 1000 - 600 = 400

Thus the required sums are Rs. 400 and Rs. 600.

#SPJ3

Answer 2

Given:

Total sum lent = 100 rupees

Rate of interest for first person = 5%

rate of interest for second person = 8 %

Total interest received = 62 rupees

To Find:

Find the sum lent to each person

Solution:

Let the sum lent to first person = x

then according to question,

sum lent to second person = 1000-x

interest =( P xR xT )/100

Interest for first person = (x . 5 .1)/100

Interest for second person = {(1000-x)8.1}/100

total interest = Interest for first person + Interest for second person

62 = 5x/100 + {(1000-x)8}/100

6200 = 5x +8000 - 8x

3x = 1800

x=600

1000-x =400

Hence the lent sums are 400 and 600 rupees.