Multiple choice

Mohan has some money (Rs. M) that he divides in the ratio of 1 : 2. He then deposits the smaller amount in a savings scheme that offers a certain rate of interest, and the larger amount in another savings scheme that offers half of that rate of interest, both interests compounded yearly. At the end of two years, the total interest earned from the two savings schemes is Rs. 830. It is known that one of the interest rates is 10% and that Mohan deposited more than Rs. 1000 in each savings scheme at the start. What is the value of M?

  1. 12,000

  2. 4,500

  3. 6,000

  4. 7,500

  5. To solve this, the other interest rate must also be given.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the amounts be x and 2x. Total M = 3x. Scheme 1 (x) at r%, Scheme 2 (2x) at r/2%. Interest = x(1 + r/100)^2 - x + 2x(1 + r/200)^2 - 2x = 830. If r=10, interest = x(1.21 - 1) + 2x(1.1025 - 1) = 0.21x + 0.205x = 0.415x = 830. x = 2000. M = 3x = 6000. If r=20, interest = x(1.44 - 1) + 2x(1.21 - 1) = 0.44x + 0.42x = 0.86x = 830, x is not an integer. Thus, 6000 is the correct value.

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