# Answers and Solutions

Question: A certain sum of money is invested for two years at a certain rate of simple interest. If the rate of interest is 6% higher, then the interest earned will be 40% more than the interest earned earlier. What is the earlier rate of interest?

Posted by: Surajit P. on 09.06.2022

Ans. 15 % p.a.

Explanation: Let, the actual rate of interest be r% p.a. and principal be Rs. 100.

So, in 1st case, after 2 yrs, the interest = Rs. 2r .

In 2nd case, rate of interest = (r + 6)% p.a.

By the problem, 2(r + 6) = (140/100)*2r  .       => 2r + 12 = 2.8r   .        =>  r = 15 .

Hence, the reqd. rate of interest = 15% p.a.

Let  the principal  =  Rs 100

Let the original  rate of simple interest =  x %

Then the total simple interest on Rs 100 per  2 years =  Rs  2x

The new interest rate is 6% more than ther original interest

Therfore the new rate of simple interest   =   (x+6)%

Hence total interest on 2 years per Rs 100 =  2(x+6)

It is given that the total interest with new rates is 40% more than the interest earned earlier.

Therfore 2(x+6) = (1.4)*2x

that is (2.8)x - 2x =  12

or (0.8) x =  12

Therfore x =  12/(0.8) = 15

Hence original rate of interest = 15%

Let i be earlier interest in %. and P be Principal.Then 1.4x2Pi/100= 2P(i+6)/100 Solving we get i=15% Ans
Let i be earlier interest in %. and P be Principal.Then 1.4x2Pi/100= 2P(i+6)/100 Solving we get i=15% Ans
Let i be earlier interest in %. and P be Principal.Then 1.4x2Pi/100= 2P(i+6)/100 Solving we get i=15% Ans
Let P rupees are invested for 2 yrs @ R interest per annum and earned Rs 100 as simple interest. 100=2*P*R÷100 5000=P*R....(1) Now if interest rate is R+6 then interest earned will be 40% more. 140=2*P*(R+6) /100 By solving this 14000=2*P*R+12P.....(2) By substituting value of PR from equation 1 in equation 2 we get P= 4000/12 Resubstituting in equation 1 5000=4000/12*R R=15% is original interest rate.
Let P rupees are invested for 2 yrs @ R interest per annum and earned Rs 100 as simple interest. 100=2*P*R÷100 5000=P*R....(1) Now if interest rate is R+6 then interest earned will be 40% more. 140=2*P*(R+6) /100 By solving this 14000=2*P*R+12P.....(2) By substituting value of PR from equation 1 in equation 2 we get P= 4000/12 Resubstituting in equation 1 5000=4000/12*R R=15% is original interest rate.
Let P rupees are invested for 2 yrs @ R interest per annum and earned Rs 100 as simple interest. 100=2*P*R÷100 5000=P*R....(1) Now if interest rate is R+6 then interest earned will be 40% more. 140=2*P*(R+6) /100 By solving this 14000=2*P*R+12P.....(2) By substituting value of PR from equation 1 in equation 2 we get P= 4000/12 Resubstituting in equation 1 5000=4000/12*R R=15% is original interest rate.
Let principal=p Rate=r,time=2 Ys According to condition 1, Interests I=(2pr)/100 According to condition 2, I+(2/5)I={2p(r+6)}/100 Or,(7/5)I={2pr/100}+(12p/100) Simplyfying the above,we get r=15
Let principal=p Rate=r,time=2 Ys According to condition 1, Interests I=(2pr)/100 According to condition 2, I+(2/5)I={2p(r+6)}/100 Or,(7/5)I={2pr/100}+(12p/100) Simplyfying the above,we get r=15
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