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A sum of Rs. 2800 is divided into two parts in such a way that the interest on both the parts is equal. If the first part is lent at 9% p.a. for 5 years and second part is for 6 years at 10% p.a., find the two sums.
1. Rs.1800, Rs.1000
2. Rs.1600, Rs.1200
3. Rs.1400, Rs.1400
4. Rs.1500, Rs.1300

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Best answer
Correct Answer - Option 2 : Rs.1600, Rs.1200

Given:

Rate (R1) = 9%, Rate (R2) = 10%

Time (T1) = 5 years, Time (T2) = 6 years

Formula Used: 

Simple Interest (I) = (P × R × T)/100 

where p = principal

R = rate

T = time 

Calculations:

Let the first part be Rs. x.

Second part = Rs.(2800 – x)

According to the question,

\(\frac{x\ ×\ 9\ ×\ 5}{100}\ =\ \frac{(2800\ -\ x)\ × \ 10\ ×\ 6}{100}\)

⇒ 45x = 60 × 2800 - 60x

⇒ 105x = 60 × 2800

⇒ x = 1600

Second part = 2800 - 1600 = 1200

∴ the correct answer is 1600 and 1200.

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