mahesh borrowed a certain sum for two years at simple interest from bhim. mahesh lent this sum to vishnu at the same rate for two years compound interest. at the end of two years, mahesh received 400 as simple interest. find the sum and rate of interest.
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Answer:
mahesh borrowed a certain sum for two years at simple interest from bhim. mahesh lent this sum to vishnu at the same rate for two years compound interest. at the end of two years, mahesh received 400 as simple interest. find the sum and rate of interest.
Step-by-step explanation:
mahesh borrowed a certain sum for two years at simple interest from bhim. mahesh lent this sum to vishnu at the same rate for two years compound interest. at the end of two years, mahesh received 400 as simple interest. find the sum and rate of interest.
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Answer:
Let the principal be P, interest rate be r and time period be n, then for the compound interest the formula will be
A=P(1+r/100)^n - P
and simple interest will be A=Pnr/100.
Mahesh borrowed a certain sum for two years at simple interest from Bhim. Mahesh lent his sum to Vishnu at the same rate for two years compound interest.
Let us assume the amount is P and the rate is r.
So, according to the formula Mahesh will pay for the simple interest
A1=P×2×r/100=400
and he will get for the compound interest
A2=P(1+r/100)2^−P=410
Simplifying A2=P(1+r/100)^2−P=410, we get
P(1+r/100+1 (1+r/100−1)=410
⇒Pr/100[(2+r/100)]=410
From A1=P×2×r/100=400, we get
Pr=20000 .
Putting the value in Pr/100(2+r/100)=410, we get
20000/100(2+r/100)=410
⇒2+r/100=410/200
⇒r/100=410/200−2
=10/200
⇒r=5
Now putting the value of r=5 in the equation of Pr=20000, we get
P×5=20000
⇒P=20000/5=4000
Therefore the sum is 4000
Therefore the sum is 4000And the Interest is 5%