Question : Deepak lent Rs. 8800 to Jaichand for 13 years and Rs. 5500 to Kapil for 12 years on simple interest at the same rate of interest and received Rs.14432 in all from both of them as interest. The rate of interest per year is:
Option 1: 8.5 percent
Option 2: 9 percent
Option 3: 9.5 percent
Option 4: 8 percent
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Correct Answer: 8 percent
Solution :
Deepak lent money to Jaichand.
The principal amount for Jaichand = 8800
Time for Jaichand
= 13 year
Deepak lent money to Kapil.
The principal amount for Kapil = 5500
Time for Kapil= T
K
= 12 year
Let rate of interest in time = $r$
Deepak lent money to Jaichand and Deepak at the same rate of interest a simple interest rate.
According to the question, money received by Deepak:
14432 = $(\frac{\text{Principal×Rate×Time}}{100})$
Jaichand
+ $(\frac{\text{Principal×Rate×Time}}{100})$
Kapil
⇒ $14432= (\frac{8800×r×13}{100}+\frac{5500×r×12}{100})$
⇒ $14432 = (1144×r) + (660×r)$
⇒ $14432 = 1804 × r$
⇒ $r = 8$%
Hence, the correct answer is 8 percent.
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