Question

if a number is increase by 20%, and decrease by 14 2/7%, and again increase by 12 1/2% then what is the final change in the number?

Answer 1

let the original number be 'x '

when the increase = 20%

Then ,

new number = x + 20% of x = 1.2x

when decrease = 14 whole 2/7%

= 100/ 7 %

then new number = 1.2x - 100/7 % of 1.2x

= 1.2x - ( 100 × 1.2x) / 700

= 1.2x - (1.2x/ 7) = (8.4x - 1.2x) / 7

= 7.2x/ 7

again ,increase = 12 whole 1/2 %

= 25 / 2 %

then ,the number obtained

= 7.2x/ 7 + (25/ 2) % of 7.2x/ 7

= (7.2x/ 7) + ( 25 × 7.2x / 2 × 7 × 100)

= (7.2x / 7 ) + (7.2x / 56)

= (7.2x × 8 + 7.2x ) / 56

= 64.8x / 56 = final number

Find the change:
-------------------------

change = Final number - original number

= (64.8x / 56) - ( x )

= 8.8x / 56

Find the % change:
-----------------------------

%change = (change × 100 ) / original number

= (8.8x × 100 ) / 56 × x

= 880/ 56 = 15.7%

Answer: change = 15.7%

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Answer 2

Let the number be x

The number is increased by 20%:

Increase = 20% of x = 20/100 x

Number = x + 20/100 x = 6/5 x

The number is decreased by 14 2/7%:

Decrease = 14 2/7% of 1.2x = (100/7 ÷ 100) x 6/5 x = 6/35 x

Number = 6/5 x - 6/35 x = 36/35 x

The number is increased by 12 1/2%:

Increase = 12 1/2 % of 36/35 x = (25/2 ÷ 100) x 36/35 x = 9/70 x

Number = 36/35 x +  9/70 x = 81/70 x

Find the change in the number:

Change = 81/70 x - x = 11/70 x

Percentage change = (11/70 x ÷ x) x 100 = 15.71%

Answer:  15.71%