Question

The price of an article was first increased by 10% and later decreased by 5%. What is the percent change in the price?

Answer 1

let the price be 100
price after increase = (110/100)×100=110
price after decrease = (95/100)×110=104.5
total increase =4.50
increased %=(4.50/100)×100=4.50%

Answer 2

The percent change in the price is 4.5%

Given :

The price of an article was first increased by 10% and later decreased by 5%

To find :

The percent change in the price

Solution :

Step 1 of 3 :

Find price after increase

Let initial price = Rs. 100

Since the price of the article was first increased by 10%

Amount of increase

$\displaystyle \sf{ =Rs. \: 100 \times \frac{10}{100} }$

$\displaystyle \sf{ =Rs. \: 10}$

After fist increase the price is

= Rs. 100 + Rs. 10

= Rs. 110

Step 2 of 3 :

Find price after decrease

The price later decreased by 5%

After decrease amount of decrease in price

$\displaystyle \sf{ =Rs. \: 110 \times \frac{5}{100} }$

$\displaystyle \sf{ =Rs. \: 5.5}$

After decrease the price

= Rs. 110 - Rs. 5.5

= Rs. 104.5

Step 3 of 3 :

Find percent change in the price

104.5 > 100

Total Amount of increase

= Rs. 104.5 - Rs. 100

= Rs. 4.5

Hence percent change in the price

$\displaystyle \sf{ = \frac{4.5}{100} \times 100\% }$

$\displaystyle \sf{ = 4.5 \: \% }$

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