Arithmetic

Simple & Compound Interest

Medium

In 4 years, an amount of ₹ 6,000 becomes ₹ 8,000 at a certain rate of simple interest. In what time at the same simple interest rate, will an amount of ₹ 525 become ₹ 700?

2 years

3 years

4 years

5 years

✅ Correct Option: 3

Principal $= ₹ 6000$

Amount $= ₹ 8000$

Thus, $\text{SI} = ₹2000$ in 4 years

$\text{SI per year} = ₹500$

$\text{Interest rate} = \dfrac{500}{6000}= \dfrac{1}{12}$

Now, to $₹525$ to become $₹700, \text{ SI}$ required is $₹ 175$

$SI = {P \times N \times R}$

$175 = {525 \times N \times \dfrac{1}{12}}$

$N = \dfrac{175 \times 12 }{525} = \dfrac{12}{3}= 4$ years.

Hence, the correct option is Option 3.

Shortcut: We observe, in 4 years, we get $\frac{1}{3}^{rd}$ principal as interest i.e. $₹ 2000$ from $₹ 6000$

Similarly, to earn $₹ 175$ on $₹525$ which is also, $\frac{1}{3}^{rd}$ of principal, it will take 4 years.

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