Question

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? [This Question was asked as TITA]

• A. 12
• B. 10
• C. 13
• D. 15

Answer 1

The Correct Option is A

To solve how many years after Veeru's investment their balances will be equal, we start by denoting:
Let \( x \) be the number of years after Veeru's investment when their balances are equal. Thus,
Veeru's time period = \( x \) years
Joy's time period = \( x-2 \) years
Since the accumulation follows simple interest, we calculate as follows:

Veeru's balance = Principal + Interest = \( 10000 + 10000 \times \frac{5}{100} \times x = 10000 + 500x \)

Joy's balance = Principal + Interest = \( 8000 + 8000 \times \frac{10}{100} \times (x-2) = 8000 + 800(x-2) = 8000 + 800x - 1600 = 6400 + 800x \)

Setting Veeru's and Joy's balances equal gives:
\[ 10000 + 500x = 6400 + 800x \]

Simplifying the equation:
\[ 10000 - 6400 = 800x - 500x \]
\[ 3600 = 300x \]
\[ x = \frac{3600}{300} \]
\[ x = 12 \]

Therefore, the balances will be equal 12 years after Veeru's investment.

Answer 2

Let the total time be \( t \) years. 

Initial investment amount by Veeru:
\( A_{\text{Veeru}} = 10,000\left(1 + \frac{5t}{100}\right) \)

Initial investment amount by Joy:
\( A_{\text{Joy}} = 8,000\left(1 + \frac{10(t - 2)}{100}\right) \)

According to the question, both investments become equal:
\( 10,000\left(1 + \frac{5t}{100}\right) = 8,000\left(1 + \frac{10(t - 2)}{100}\right) \)

Remove the brackets and simplify:
\( 10,000\left(1 + \frac{5t}{100}\right) = 8,000\left(1 + \frac{10t - 20}{100}\right) \)
\( 10,000\left(\frac{100 + 5t}{100}\right) = 8,000\left(\frac{100 + 10t - 20}{100}\right) \)
\( 10,000\left(\frac{100 + 5t}{100}\right) = 8,000\left(\frac{80 + 10t}{100}\right) \)

Multiply both sides by 100 to remove the denominator:
\( 10,000(100 + 5t) = 8,000(80 + 10t) \)

Expand both sides:
\( 1,000,000 + 50,000t = 640,000 + 80,000t \)

Bring like terms together:
\( 1,000,000 - 640,000 = 80,000t - 50,000t \)
\( 360,000 = 30,000t \)

Solving for \( t \):
\( t = \frac{360,000}{30,000} = 12 \)

So, the correct answer is: 12 years (Option A).