#### Ahmed purchased an old scooter for ₹ 16000. If the cost of the scooter after 2 years depreciates to ₹ 14440, find the rate of depreciation.

**Solution:**

It is given that

Present value = ₹ 16000

Value after 2 years = ₹ 14440

Consider r% p.a. as the rate of depreciation

We know that

A/P = (1 – r/100)^{n}

Substituting the values

14440/16000 = (1 – r/100)^{2}

By further calculation

361/400 = (1 – r/100)^{2}

(19/20)^{2} = (1 – r/100)^{2}

We can write it as

1 – r/100 = 19/20

So we get

r/100 = 1 – 19/20 = 1/20

By cross multiplication

r = 1/20 × 100 = 5%

Hence, the rate of depreciation is 5%.

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