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Question

Reena borrowed from Kamila certain sum for two years at simple interest Reena lent this to Hamin at the same rate for two years compound interest At the end of two years she received Rs 110 as compound interest but paid Rs 100 as simple interest Find the sum and rate of interest

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Solution

The correct option is **C** Rs 250 and 20%

Simple interest for two years= Rs. 100

∴Interest per year=Rs.50

By compound interest

Interest for I year=Rs.50

Interest for II year=Rs.(110−50)=Rs.60

=50+20% of 50=Rs.60

∴Rate of interest=20%

Let sum borrowed by Reena be P

⇒S.I=PTR100

⇒100=P×2×20100

⇒P=100×1002×20

⇒P=250

∴Sum borrowed=Rs.250

Rate of interest=20%

Simple interest for two years= Rs. 100

∴Interest per year=Rs.50

By compound interest

Interest for I year=Rs.50

Interest for II year=Rs.(110−50)=Rs.60

=50+20% of 50=Rs.60

∴Rate of interest=20%

Let sum borrowed by Reena be P

⇒S.I=PTR100

⇒100=P×2×20100

⇒P=100×1002×20

⇒P=250

∴Sum borrowed=Rs.250

Rate of interest=20%

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