Question 15 Marks
A sum amounts to Rs. 2,652 in 6 years at 5% p.a. simple interest. Find:
(i) the sum
(ii) the time in which the same sum will double itself at the same rate of interest.
(i) the sum
(ii) the time in which the same sum will double itself at the same rate of interest.
Answer
View full question & answer→(i) In First case, Let principal $(P)=$ rs. 100
Rate $(R)=5 \%$ p.a., Time $(T)=6$ years
$ \begin{aligned} & \therefore \text { S.I. }=\frac{\mathrm{P} \times \mathrm{R} \times \mathrm{T}}{100} \\ & =\frac{100 \times 5 \times 6}{100}=\text { Rs. } 30 \end{aligned} $
and, amount $=$ Rs. $100+$ Rs. $30=$ Rs. 130
If amount is Rs. 130 , then principal $=$ Rs. 100
and, if amount is Rs. 2652, then principal
$ =\frac{100 \times 2652}{130}=\text { Rs. } 2040 $
In second case, Let sum $(P)=$ Rs. 100
Amount $(A)=$ Rs. $100 \times 2=$ Rs. 200
$ \text { S.I. }=\text { A - P = Rs. } 200-100=\text { Rs. } 100 $
Rate $=5 \%$ p.a.
$ \text { Time }=\frac{\text { S.I. } \times 100}{P \times R}=\frac{100 \times 100}{100 \times 5}=20 \text { years } $
Rate $(R)=5 \%$ p.a., Time $(T)=6$ years
$ \begin{aligned} & \therefore \text { S.I. }=\frac{\mathrm{P} \times \mathrm{R} \times \mathrm{T}}{100} \\ & =\frac{100 \times 5 \times 6}{100}=\text { Rs. } 30 \end{aligned} $
and, amount $=$ Rs. $100+$ Rs. $30=$ Rs. 130
If amount is Rs. 130 , then principal $=$ Rs. 100
and, if amount is Rs. 2652, then principal
$ =\frac{100 \times 2652}{130}=\text { Rs. } 2040 $
In second case, Let sum $(P)=$ Rs. 100
Amount $(A)=$ Rs. $100 \times 2=$ Rs. 200
$ \text { S.I. }=\text { A - P = Rs. } 200-100=\text { Rs. } 100 $
Rate $=5 \%$ p.a.
$ \text { Time }=\frac{\text { S.I. } \times 100}{P \times R}=\frac{100 \times 100}{100 \times 5}=20 \text { years } $