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A sum of Rs. 10 is lent to be returned in 11 monthly instalments of Rs. 1 each, interest being simple. The rate of interest is:
Answer & Solution
Correct Answer:
Option
D
⇒ Rs. 10 + S.I. on Rs. 10 for 11 months
= Rs. 11 + S.I. on Rs. 1 for (1 + 2 + 3 + 4 + ........... + 10) months
⇒ Rs. 10 + S.I. on Rs. 1 for 110 months
= Rs. 11 + S.I. on Rs. 1 for 55 months
S.I. on Rs. 1 for 55 months = Rs. 1
$$\eqalign{ & \therefore {\text{Rate}} = \left( {\frac{{100 \times 12}}{{1 \times 55}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 21\frac{9}{{11}}\% \cr} $$
= Rs. 11 + S.I. on Rs. 1 for (1 + 2 + 3 + 4 + ........... + 10) months
⇒ Rs. 10 + S.I. on Rs. 1 for 110 months
= Rs. 11 + S.I. on Rs. 1 for 55 months
S.I. on Rs. 1 for 55 months = Rs. 1
$$\eqalign{ & \therefore {\text{Rate}} = \left( {\frac{{100 \times 12}}{{1 \times 55}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 21\frac{9}{{11}}\% \cr} $$
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