Nitu has an initial capital of ₹20,000. Out of this, she invests ₹8,000 at 5.5% in bank A, ₹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:
Question:
Nitu has an initial capital of ₹20,000. Out of this, she invests ₹8,000 at 5.5% in bank A, ₹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:
Nitu has an initial capital of ₹20,000. Out of this, she invests ₹8,000 at 5.5% in bank A, ₹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:
Options
Answer: 800
Explanation:
Step 1: Define knowns and unknown Nitu's initial capital = ₹20,000 Investment details: Bank A: ₹8,000 at 5.5% per annum (simple interest) Bank B: ₹5,000 at 5.6% per annum (simple interest) Bank C: remaining amount = ₹20,000 - ₹8,000 - ₹5,000 = ₹7,000 at x% per annum (simple interest) Combined annual interest = 5% of initial capital = 5% of 20,000 = ₹1,000 We are asked: If the entire ₹20,000 were invested in bank C at x%, what would be the annual interest? Step 2: Write equation for total interest Total interest = Interest from A + Interest from B + Interest from C = 1,000 Interest from A = 8,000 × 5.5 / 100 = 440 Interest from B = 5,000 × 5.6 / 100 = 280 Interest from C = 7,000 × x / 100 = 70 x Equation: 440 + 280 + 70 x = 1,000 Step 3: Solve for x 440 + 280 = 720 720 + 70 x = 1,000 70 x = 280 x = 4 So bank C's rate = 4% per annum Step 4: Compute interest if entire capital invested in bank C Entire capital = 20,000 Rate = 4% per annum Interest = 20,000 × 4 / 100 = ₹800
Explanation:
Step 1: Define knowns and unknown Nitu's initial capital = ₹20,000 Investment details: Bank A: ₹8,000 at 5.5% per annum (simple interest) Bank B: ₹5,000 at 5.6% per annum (simple interest) Bank C: remaining amount = ₹20,000 - ₹8,000 - ₹5,000 = ₹7,000 at x% per annum (simple interest) Combined annual interest = 5% of initial capital = 5% of 20,000 = ₹1,000 We are asked: If the entire ₹20,000 were invested in bank C at x%, what would be the annual interest? Step 2: Write equation for total interest Total interest = Interest from A + Interest from B + Interest from C = 1,000 Interest from A = 8,000 × 5.5 / 100 = 440 Interest from B = 5,000 × 5.6 / 100 = 280 Interest from C = 7,000 × x / 100 = 70 x Equation: 440 + 280 + 70 x = 1,000 Step 3: Solve for x 440 + 280 = 720 720 + 70 x = 1,000 70 x = 280 x = 4 So bank C's rate = 4% per annum Step 4: Compute interest if entire capital invested in bank C Entire capital = 20,000 Rate = 4% per annum Interest = 20,000 × 4 / 100 = ₹800
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