Multiple choice

A sum of Rs. 32000 is partly lent at simple interest and the remaining at compound interest for a period of two years in both cases. The rate of interest is 10% p.a. and the total interest earned at the end of two years is Rs. 6550. What is the sum lent at compound interest? 32000 रू. की राशि को अंशतः साधारण ब्याज पर उधार दिया गया है और शेष को चक्रवृद्धि ब्याज पर उधार दिया गया है जबकि दोनों 2 वर्ष के लिए देय है। ब्याज की दर 10% वार्षिक है और दो वर्ष के अन्त में कुल ब्याज 6550 रू. है। चक्रवृद्धि ब्याज पर दी गई राशि क्या है?

  1. 12000

  2. 18000

  3. 15000

  4. 20000

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the sum lent at compound interest be x. Then sum at simple interest = 32000 - x. SI for 2 years at 10% = (32000 - x) × 10 × 2/100 = 6400 - 0.2x. CI for 2 years at 10% = x[(1 + 10/100)² - 1] = x(1.21 - 1) = 0.21x. Total interest: 6400 - 0.2x + 0.21x = 6550. So 6400 + 0.01x = 6550, giving 0.01x = 150 and x = 15000.