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Question
If A is increased by 20%, it equals B. If B is decreased by 50%, it equals C. Then ______ % of A is equal to C.
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Solution
If A is increased by 20%, it equals B. If B is decreased by 50%, it equals C. Then 60 % of A is equal to C.
Explanation:
Given, If A is increased by 20%, then it is equal to B.
∴ A + 20% of A = B
⇒ `A(1 + 20/100) = B`
⇒ `120/100 A = B`
⇒ `B = 6/5 A` ...(i)
If B is decreased by 50%, then it is equal to C.
∴ B – 50% of B = C
⇒ `B(1 - 50/100) = C`
⇒ `B xx 50/100 = C`
⇒ `1/2 B = C`
⇒ B = 2C ...(ii)
On comparing equations (i) and (ii), we get
`6/5 A = 2C`
⇒ `A/C = 10/6`
⇒ `C = 6/10`
⇒ `C = 3/5 A`
∴ In percentage, `C/A xx 100 = (3/5 A)/A xx 100%`
= `3/5 xx 100%`
= 60%
Hence, 60% of A is equal to C.
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