A and B invest in a scheme which provides simple interest at the rate of 5 and 6 percent per annum for initial capitals less and greater than Rs 21000 respectively. B’s capital is 20% more than that of A who invests Rs 20000. If B invests for two and half years, for how many additional days above three years (the fourth year being a non-leap year) should A invest so that she earns the same amount of interest as B

1. 219
2. 73
3. 146
4. 292

Solution

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Correct option is A. 219

Let’s break down the information provided in the problem:

1. A invests Rs 20,000 at a 5% simple interest rate per annum.
2. B’s capital is 20% more than A’s capital, which means B invests 1.20 × 20,000 = Rs 24,000 at a 6% simple interest rate per annum.
3. B invests for 2.5 years.

Now, we need to find out for how many additional days above three years A should invest so that A earns the same amount of interest as B.

First, let’s calculate the interest earned by B:

Interest = Principal × Rate × Time Interest_B = 24,000 × 6% × 2.5 Interest_B = 24,000 × 0.06 × 2.5 Interest_B = Rs 3,600

Now, let’s find out the interest earned by A in 3 years:

Interest_A_3_years = 20,000 × 5% × 3 Interest_A_3_years = 20,000 × 0.05 × 3 Interest_A_3_years = Rs 3,000

Now, we need to find out the additional interest that A needs to earn to match B’s interest:

Additional_Interest_A = Interest_B – Interest_A_3_years Additional_Interest_A = 3,600 – 3,000 Additional_Interest_A = Rs 600

Now, let’s find out for how many days A needs to invest to earn this additional interest:

Since A’s interest rate is 5% per annum, let’s find out the daily interest rate:

Daily_Interest_Rate_A = (5% / 365) = 0.05 / 365 = 0.0001369863

Now, let’s find out the number of days required for A to earn the additional interest:

Number_of_Days = Additional_Interest_A / (Principal × Daily_Interest_Rate_A) Number_of_Days = 600 / (20,000 × 0.0001369863) Number_of_Days = 600 / 2.739726 Number_of_Days ≈ 219

So, A should invest for an additional 219 days over three years to earn the same amount of interest as B. The correct answer is: 219