Question

The partners A and B together lent ₹3,903@ 4%p.a. interest compounded annually. After a span of 7 years, A gets the same amount as B gets after 9 years .The share of A in the sum if₹3,903 would have been the answer is ₹2,028 i want proper explanation​

Answer 1

Here is your answer

Dear Student,

Please find below the solution to the asked query:
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The compound interest formula:A=P(1+rn)nt

Let the principal by A be x.
Then that by B would be (3903−x).

Here n=1, as the interest is compounded annually.

The rate of interest, r=4100=0.04

The amount received by A after t=7 years,
A=P(1+rn)ntA=x⋅(1+0.041)1×7A=x⋅(1.04)7

Similarly, the amount received by B after 9 years,A=(3903−x)(1+0.041)1×9A=(3903−x)(1.04)9

It is stated that the amounts are equal. Then,x⋅(1.04)7=(3903−x)(1.04)9

Dividing throughout by (1.04)7,x=(3903−x)(1.04)2x=(3903−x)×1.0816x=3903×1.0816−1.0816x2.0816x=4221.4848x=4221.48482.0816=2028

Share of A in the original investment=Rs. 2028
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Hope that is correct.

Answer 2

Answer:

The partners A and B together lent ₹3,903@ 4%p.a. interest compounded annually. After a span of 7 years, A gets the same amount as B gets after 9 years . The share of A in the sum if₹3,903 would have been the answer is ₹2,028 i want proper explanation,