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Mohan lent some amount of money at $9 %$ simple interest and an equal amount of money at $10 %$ simple interest each for $2$ years. If his total interest was Rs. $760$ , what amount was lent in each case?

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Rs.

1700

Rs.

1800

Rs.

1900

Rs.

2000

answer is D.

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Detailed Solution

Given that, Mohan lent some amount of money at

9 %

simple interest and an equal amount of money at

10 %

simple interest each for

2

years an his total interest was Rs.

760

.
We know that Simple interest =

\frac{P \times R \times T}{100},

where P = principal, T = time, R = rate.
Let the amount lent in each case be Rs.

x

∴ P₁ = P₂ = x

From the given,

R₁ = 9, R₂ = 10, T₁ = T₂ = 2

∴ Total Interest

= \frac{P₁ \times R₁ \times T₁}{100} + \frac{P₂ \times R₂ \times T₂}{100}

\Rightarrow 760 = \frac{x \times 9 \times 2}{100} + \frac{x \times 10 \times 2}{100}

\Rightarrow 760 = \frac{18 x}{100} + \frac{20 x}{100}

\Rightarrow 38 x = 76000

\Rightarrow x = Rs . 2000

Thus, the amount lent is Rs.2000.
Therefore, the correct option is 4.

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