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A man had $Rs . 2, 000$ . He lent a part of this at $5 %$ interest and the rest at $4 %$ interest. The total interest he received in one year was $Rs . 92$ . The money he lent at $5 %$ interest was

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Rs . 1, 350

Rs . 1, 200

Rs . 1, 300

Rs . 1, 250

answer is A.

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Detailed Solution

Given,
Amount man had = Rs. 2000
He lent a part of this amount at

5 %

interest and the rest at

4 %

interest.
Interest received in a year = Rs.92
Let the money lent at the rate of

5 %

x .

So, the money lent at

4 %

will be (

2000 - x) .

We know,

Interest = \frac{P \times R \times T}{100}

, where P = principal, R = rate, T = time.
Then,
Interest at 5% in one year =

\frac{x \times 5 \times 1}{100}

\Rightarrow

Interest at 5% in one year = 0.05

x

Now,
Interest at 4% in one year

= \frac{(2000 - x) \times 4 \times 1}{100}

\Rightarrow

Interest at 4% in one year

= 0.04 (2000 - x)

It is given that the total interest obtained in

1

year is

Rs . 92 .

∴

92 = 0.05 x + 0.04 (2000 - x)

\Rightarrow 92 = 0.05 x + 80 - 0.04 x

⇒

92 = 80 + 0.01 x

⇒

0.01 x = 12

⇒

x = 1200

Hence, the money lent at

5 %

rate was

Rs . 1200 .

Therefore, the correct option is 1.

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