Arithmetic

Simple & Compound Interest

Medium

Veeru invested Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10% simple annual interest. How many years after Veeru's investment, will their balances, i.e., principal plus accumulated interest, be equal?

Entered answer:

✅ Correct Answer: 12

We understand what's happening:

Veeru invests Rs 10000 at 5% simple interest (starts immediately)

Joy invests Rs 8000 at 10% simple interest (starts exactly 2 years later)

We need to find when their total amounts will be equal

For simple interest, the total amount after time $t$ is:

Amount = Principal + Interest

Amount = Principal + (Principal × Rate × Time)/100

This can be written as: Amount = P(1 + rt/100)

Let $x$ = number of years after Veeru's investment when both amounts are equal

Key insight: When Veeru has been investing for $x$ years, Joy has only been investing for $(x-2)$ years because Joy started 2 years later.

Veeru's amount after $x$ years:

Principal = Rs 10000

Rate = 5% per year

Time = $x$ years

Amount = $10000 + 10000 \times \dfrac{5x}{100} = 10000 + 500x$

Joy's amount after $x$ years from Veeru's start:

Principal = Rs 8000

Rate = 10% per year

Time = $(x-2)$ years (since Joy started 2 years later)

Amount = $8000 + 8000 \times \dfrac{10(x-2)}{100} = 8000 + 800(x-2)$

When their amounts are equal:

$10000 + 500x = 8000 + 800(x-2)$

Expanding the right side:

$10000 + 500x = 8000 + 800x - 1600$

Simplifying the right side:

$10000 + 500x = 6400 + 800x$

Moving all terms with $x$ to one side:

$10000 - 6400 = 800x - 500x$

$3600 = 300x$

$x = \dfrac{3600}{300} = 12$

12 years after Veeru's investment, both their balances will be equal at Rs 16000 each.

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