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.

Answer 1

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.