Question

David lent a certain sum to two persons at simple interest. He lent Rs. 2000 more to the first person than he did to the second person. The rates of interest at which David lent to the first and second person are 12% and 10% p.a respectively. The interest received from the first person in 2 years equals that received from the second person in 3 years. Find the money lent to the first person.

Answer 1

The money lent to the first person is 10000 Rs.

Step-by-step explanation:

If the amount is P, annual rate of interest r and period n years then we know that simple interest is

$I=\frac{nPr}{100}$

Let the amount that David lent to the second person is X Rs.

Then the amount he lent to the first person = (X + 2000) Rs.

Rate of interest to the first person  = 12%

Rate of interest to the second person  = 10%

The interest received from the first person in 2 years is equal to the second person in 3 years

Therefore,

$\frac{2\times 12\times (X+2000)}{100}=\frac{3\times 10\times X}{100}$

$\implies 24(X+2000)=30X$

$\implies 24X+2000\times 24=30X$

$\implies 6X=24\times 2000$

$\implies X=4\times 2000$

$\implies X=8000$

Thus, the money lent to the first person = 8000 + 2000 = 10000 Rs.

Hope this answer is helpful.

Know More:

Q: Ramesh lent rs.2500 to his two friends.He gave rs.10000 at 10% p.a. simple interest to one of his friends the remaining to other at 12 % p.a.How much interest did he receive in after two years?

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Q: A person lent a certain sum of money at 4% simple interest and in 8 years the interest amount to Rs340 less than the sum lent find the sum lent .

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Answer 2

Answer:

10,000

Step-by-step explanation: