Quantitative Aptitude – Arithemetic – Interest – Mohan has some money


XAT 2021 Exam Paper – Quantitative Aptitude – Arithemetic – Interest – Mohan has some money

Q. Mohan has some money (₹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 compound yearly. At the end of two years, the total interest earned from the two savings schemes is ₹830. It is known that one of the interest rates is 10% and that Mohan deposited more than ₹1000 in each saving scheme at the start. What is the value of M?
  1. 12000
  2. 4500
  3. 6000
  4. 7500
  5. To solve this, the other interest rate must also be given

Answer: 6000

Solutions:
Let the smaller amount be x and larger amount be 2x such that x > 1000.
So total money ( M ) = 3x .
Case 1: rate of interest on smaller amount = 10
rate of interest on larger amount = 5
Total interest received = (1.1^2 – 1)*x + (1.05^2 – 1)*2x = 0.21x + 0.205x
Given, 0.21x + 0.205x = 830
=> 415x = 830000
=>x= 2000
So M = 3x = 6000
Case 2:
rate of interest on smaller amount = 20
rate of interest on larger amount = 10
Total interest received = (1.2^2 – 1)*x+(1.1^2 – 1)*2x = 0.44x + 0.42x
Given, 0.44x+0.42x = 830=> x = 965.11
Which is not valid since x is greater than 1000
Thus M = 6000


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