Discussion

Question:

Nitu has an initial capital of Rs. 20,000. Out of this, she invests Rs. 8,000 at 5.5% in bank A, Rs. 5,000 at 5.6% in bank B and the remaining amount at x% in bank C, each rate being simple interest per annum. Her combined annual interest income from these investments is equal to 5% of the initial capital. If she had invested her entire initial capital in bank C alone, then her annual interest income, in rupees, would have been

Explanation:

Rs. 8000 is invested at 5.5% earning yearly interest of 8000 × 5.5% = Rs. 440
Rs. 5000 is invested at 5.6% earning yearly interest of 5000 × 5.6% = Rs. 280
Rs. 7000 is invested at x% earning yearly interest of 7000 × x% = Rs. 70x

Overall, 20,000 is invested which earns 5% yearly interest = 5% of 20000 = 1000

⇒ 440 + 280 + 70x = 1000
⇒ 70x = 1000 – 720 = 280
⇒ x = 4%

∴ If she had invested her entire initial capital in bank C alone, then her annual interest income = 4% of 20000 = Rs. 800
Hence, option (a).

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