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CAT 2024 Slot 1 — QA Question 13

Simple InterestEasy

An amount of Rs 10000 is deposited in bank A for a certain number of years at a simple interest of 5% per annum. On maturity, the total amount received is deposited in bank B for another 5 years at a simple interest of 6% per annum. If the interests received from bank A and bank B are in the ratio 10 : 13, then the investment period, in years, in bank A is

Answer & solution

  • 6

  • B

    5

  • C

    3

  • D

    4

Solution

Medium

Let the time in bank A be tt years. Compute bank A's interest, then the maturity amount that gets re-deposited, then bank B's interest over 55 years. Set the ratio of the two interests to 10:1310:13 and solve for tt.

1

Bank A interest and maturity. Principal 1000010000 at 5%5\% for tt years.

IA=10000×5100×t=500t⇒ Maturity PB=10000+500t(deposited in B)\begin{aligned} &I_A=10000\times\tfrac{5}{100}\times t=500t\\ &\Rightarrow\ \text{Maturity }P_B=10000+500t \quad\text{(deposited in B)} \end{aligned}
2

Bank B interest. Principal PBP_B at 6%6\% for 55 years.

IB=(10000+500t)×6100×5⇒ IB=0.3 (10000+500t)=3000+150t(simplify)\begin{aligned} &I_B=(10000+500t)\times\tfrac{6}{100}\times5\\ &\Rightarrow\ I_B=0.3\,(10000+500t)=3000+150t \quad\text{(simplify)} \end{aligned}
3

Apply the ratio IA:IB=10:13I_A:I_B=10:13 using steps 1 and 2.

500t3000+150t=1013⇒ 6500t=10(3000+150t)(cross-multiply)⇒ 6500t=30000+1500t⇒ 5000t=30000 ⇒ t=6\begin{aligned} &\dfrac{500t}{3000+150t}=\dfrac{10}{13}\\ &\Rightarrow\ 6500t=10(3000+150t) \quad\text{(cross-multiply)}\\ &\Rightarrow\ 6500t=30000+1500t\\ &\Rightarrow\ 5000t=30000\ \Rightarrow\ t=6 \end{aligned}
t=6 yearst=6\text{ years}
CAT 2024 Slot 1 QA Q13: An amount of Rs 10000 is deposited in bank A for a certain number of years at a simple interest of 5% per annu — Solution | TheCATExam