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ICSE Class 10 Mathematics Question 4 of 49

Multiple-Choice Questions — Question 4

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Question

Question 4

Anwesha intended to open a Recurring Deposit account of ₹ 1000 per month for 1 year in a Bank, paying a 5% per annum rate of simple interest. The bank reduced the rate to 4% per annum. How much must Anwesha deposit monthly for 1 year so that her interest remains the same?

  1. ₹ 12325

  2. ₹ 1250

  3. ₹ 1200

  4. ₹ 1000

Answer

In first case :

P = ₹ 1000

r = 5%

n = 12 months

Interest = P×n(n+1)2×12×r100P \times \dfrac{n(n + 1)}{2 \times 12} \times \dfrac{r}{100}

=1000×12×(12+1)2×12×5100=1000×12×132×12×120=25×13=₹325.= 1000 \times \dfrac{12 \times (12 + 1)}{2 \times 12} \times \dfrac{5}{100} \\[1em] = 1000 \times \dfrac{12 \times 13}{2 \times 12} \times \dfrac{1}{20} \\[1em] = 25 \times 13 \\[1em] = ₹ 325.

In second case :

P = ₹ x (Let)

r = 4%

n = 12 months

Interest = ₹ 325

∴325=x×12×132×12×4100⇒325=x×132×125⇒x=325×25×213⇒x=1625013=₹ 1250.\therefore 325 = x \times \dfrac{12 \times 13}{2 \times 12} \times \dfrac{4}{100} \\[1em] \Rightarrow 325 = x \times \dfrac{13}{2} \times \dfrac{1}{25}\\[1em] \Rightarrow x = \dfrac{325 \times 25 \times 2}{13} \\[1em] \Rightarrow x = \dfrac{16250}{13} = \text{₹ 1250.}

Hence, Option 2 is the correct option.