XAT 2021 Question 3

Question 3

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?

Solution

Let the total amount be 3x

Case 1: 

Smaller amount = x, rate of interest = 10

Larger amount = 2x, rate of interest = 5

Total amount received at the end of two years( smaller amount) = $$x\left(1+\frac{10}{100}\right)^2\ =\ 1.21x$$. CI = 0.21x

Total amount received at the end of two years( larger amount) = $$2x\left(1+\frac{5}{100}\right)^2\ =\ 2.205x$$   CI = 0.205x

Given, 0.21x + 0.205x = 830

=> x = 2000

2x= 4000

Case 2:

Smaller amount = x, rate of interest = 20

Larger amount = 2x, rate of interest = 10

Total amount received at the end of two years( smaller amount) = $$x\left(1+\frac{20}{100}\right)^2\ =\ 1.44x$$. CI = 0.44x

Total amount received at the end of two years( larger amount) = $$2x\left(1+\frac{10}{100}\right)^2\ =\ 2.42x$$ CI = 0.42x

Given, 0.44x+0.42x = 830

=> x = 965.11 which is not valid since it should be greater than 1000



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