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A sum of rs10 is lent  to be returned in 11 monthly instalments of re. 1 each , interest being simple. The rate of interest is.

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this is a nice problem on simple interest

Let the rate of interest be R% per annum

Total Amount (if paid at the end of 11 months) = P + {P*R*T/100}

= 10 + {10*R*(11/12)}/100 = 10 +11*R/120..............................(1)

Total effective payment
= (Rs.1 + interest on Rs.1 for 10 months) + (Rs.1 + interest on Rs.1 for 9 months) + ... + (Rs.1 + interest on Rs.1 for 1 month) + Rs.1

= [1 + {1*R*(10/12)}/100] + [1 + {1*R*(9/12)}/100] + .... ...+ [1 + {1*R*(1/12)}/100] + 1

=(1 + 10*R/1200) + (1 + 9*R/1200) +............+ (1 + R/1200)  + 1

=11 + R(1+2+⋯+10) / 1200

= 11 + R * (10*11/2) / 1200

11 + 11*R/240................................................................(2)

so Now we have

from (1) and (2)

10+{11*R/120}=11+{11*R/240}

here we get R = 240 /11 = 21.81 %

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