What is the principal sum ? I. The sum amounts to ` 690 in 3 years at S.I. II. The sum amounts to ` 750 in 5 years at S.I. III. The rate of interest is 5% p.a.
(a)I and III only
(b)II and III only
(c)I and II only
(d)I and III only, or II and III only
(e)Any two of the three
Answer
Answer (as printed): E
Explanation
Let the sum be ₹ $x$. From $\mathrm{I}$ and III, we have: $A=₹ 690, T=3 \mathrm{yrs}, R=5 \%$. $$\begin{aligned} \therefore \quad x+\frac{x \times 5 \times 3}{100}=690 & \Rightarrow x+\frac{3 x}{20}=690 \Rightarrow \frac{23 x}{20}=690 \\ & \Rightarrow x=\frac{690 \times 20}{23}=600 \end{aligned}$$ From II and III, we have: $\mathrm{A}=₹ 750, T=5 \mathrm{yrs}, R=5 \%$ $$\begin{aligned} \therefore \quad x+\frac{x 5 \times 5 \times 5}{100}=750 & \Rightarrow x+\frac{x}{4}=750 \Rightarrow \frac{5 x}{4}=750 \\ & \Rightarrow x=\frac{750 \times 4}{5}=600 . \end{aligned}$$ From I and II, we have: Let the rate be R\% p.a. Then, $\quad x+\frac{x \times R \times 3}{100}=690 \Rightarrow x\left(1+\frac{3 R}{100}\right)=690$ $$\text { And, } x+\frac{x \times R \times 5}{100}=750 \Rightarrow x\left(1+\frac{5 R}{100}\right)=750$$ Dividing (ii) by (i), we get: $\frac{\left(1+\frac{5 R}{100}\right)}{\left(1+\frac{3 R}{100}\right)}=\frac{750}{690}$ $\Rightarrow \quad 69(1000+5 R)=75(1000+3 R)$ $\Rightarrow \quad 120 R=600 \Rightarrow R=5$. Putting $R=5$ in (i), we get: $x\left(1+\frac{15}{100}\right)=690$ $\Rightarrow \quad x=\frac{690 \times 100}{115}=600$. Clearly, any two of the three will give us the answer. ∴ Correct answer is (e).