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Karan and Arjun divided a sum of Rs 7 lakh in the ratio of 5 ∶ 2 respectively. Karan invested the received amount at 5% per annum on simple interest. Arjun invested in the same scheme 18 months after Karan invested. After 10 years of Karan's investment, the ratio of their interests will be:
1. 17 ∶ 50
2. 71 ∶ 50
3. 50 ∶ 71
4. 50 ∶ 17

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Correct Answer - Option 4 : 50 ∶ 17

Given:

Amount Karan had = 7 × 5/7 = 5 lakhs

Amount Arjun had = 7 × 2/7 = 2 lakhs

Rate of interest = 5%

Formula:

Let P = Principle, R = rate of interest and N = time period

Simple interest = PNR/100

Calculation:

Time period for which Karan invested = 10 years

Time period for which Arjun invested = 10 - 18/12 = 17/2

Simple interest Karan will get = 5 × 10 × 5/100 = Rs.2.5 lakhs

Simple interest Arjun get = 2 × 17/2 × 5/100 = Rs.0.85 lakhs

∴ Required ratio = 2.5 : 0.85 = 50 : 17

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