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If a person borrows money at a compound interest for 3 years, then calculate the amount to be returned in 3 years. I. After 5 years, Rs. 800 has to be paid as simple interest. II. The interest is rated at 5% per annum. III. The amount to be paid after 3 years as simple interest is equal to 6 times the amount when it was borrowed. Which statement(s) is/are required to answer the question?

If a person borrows money at a compound interest for 3 years, then calculate the amount to be returned in 3 years. I. After 5 years, Rs. 800 has to be paid as simple interest. II. The interest is rated at 5% per annum. III. The amount to be paid after 3 years as simple interest is equal to 6 times the amount when it was borrowed. Which statement(s) is/are required to answer the question? Correct Answer Statement I and either statement II or statement III together are sufficient to answer the question.

Considering statements I and II together

S.I. after 1 year will be 800/5 = Rs. 160

r = 5% and t = 1 year

⇒ P = 160 × 100/5 = 3200

∵ We have Rate, Time and Principal

 Required amount can be calculated.

 Both the statements I and II together are sufficient.

Considering statements II and III together

r = 5%

S.I. = 6P

∵ The principal can not be calculated

∴ Both II and III together are not sufficient to answer the question.

Considering statements I and III together

S.I. = 6P

⇒ PRT/100 = 6P

⇒ 3R/100 = 6

⇒ R = 200%

S.I. = PRT/100

800 = P × 200 × 5/100

P = 80

∵ We have Principal, Rate and Time

 Required amount can be calculated.

∴ Both I and III together are also not sufficient to answer the question

⇒ Statement I and either statement II or statement III together are sufficient to answer the question.

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