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Question
Ankita's Salary was reduced by 50%. Again the reduced salary was increased by 50%. Find loss in terms of percentage.
Solution
Let Ankita’s initial salary be ₹ ‘x’.
Her salary was reduced by 50%.
∴ Ankita’s salary after the reduction
= `"x"(1 - 50/100) = "x"(1 - 1/2)`
= `"x"/2`
Ankita’s reduced salary was then increased by 50%
∴ Ankita’s final salary after the increase
= `"x"/2(1 + 50/100) = "x"/2(1 + 1/2)`
= `"x"/2 xx 3/2`
= `(3"x")/4`
∴ Loss in Ankita’s salary after the decrease and increase
= `"x" - (3"x")/4 = "x"/4`
Percentage loss = `"loss in salary"/"initial salary" xx 100`
= `("x"/4)/"x" xx 100`
= `1/4 xx 100`
= 25
∴ Ankita lost 25% of her salary.
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