Question : A number is first decreased by 28% and then increased by 28%. The number so obtained is 784 less than the original number. Find the value of the original number.
Option 1: 1000
Option 2: 15000
Option 3: 10000
Option 4: 1500
Correct Answer: 10000
Solution :
Given: A number is first decreased by 28% and then increased by 28%.
We know that,
Successive percentage change = $x + y + \frac{xy}{100}$
Here $x = -28$ and $y = 28$
= $-28 + 28 -\frac{28 \times 28}{100}$
= –7.84
The number will decrease by 7.84%
7.84% of the original number = 784
⇒ $\frac{7.84}{100}\times$ Original Number = 784
⇒ Original Number = 100 × 100
= 10000
Hence, the correct answer is 10000.
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