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.