IPMAT Rohtak 2019 (QA) - Veena has to pay Rs. 2460 to Sita, 5 months later at 6% simple interest per annum, and Gita has to pay Sita the same amount at 7.5% simple interest per annum after certain months. If both took the same amount of loan from Sita then Gita paid the loan after how many months? | PYQs + Solutions

IPMAT Rohtak 2019

Arithmetic

Simple & Compound Interest

Easy

Veena has to pay Rs. 2460 to Sita, 5 months later at 6% simple interest per annum, and Gita has to pay Sita the same amount at 7.5% simple interest per annum after certain months. If both took the same amount of loan from Sita then Gita paid the loan after how many months?

3 Months

4 Months

6 Months

12 Months

Correct Option: 2

Let the principal amount be

P

(same for both Veena and Gita)

For Veena:

\newline

\text{Amount} = 2460

(because question says that's the amount Veena has to pay to Sita)

\newline

\text{Time} = 5 \text{ months} = \frac{5}{12} \text{ years}

\newline

\text{Rate} = 6\%

\newline

2460 = P(1 + \frac{6 \times 5}{12 \times 100})

2460 = P(1 + \frac{30}{1200})

2460 = P(1 + \frac{1}{40})

2460 = P(\frac{41}{40})

P = 2460 \times \frac{40}{41} = 2400

For Gita:

\newline

\text{Amount} = 2460

\newline

\text{Principal} = 2400

\newline

\text{Rate} = 7.5\%

Using formula: (works for S.I. too)

\newline

A = P(1 + \frac{RT}{100})

2460 = 2400(1 + \frac{7.5T}{1200})

where

T

is time in months

\frac{2460}{2400} = 1 + \frac{7.5T}{1200}

1.025 = 1 + \frac{7.5T}{1200}

0.025 = \frac{7.5T}{1200}

T = \frac{0.025 \times 1200}{7.5} = 4

Therefore, Gita paid the loan after

4

months.