Question

The price of Hand-sanitizer is first increased by 10% , then increased by Rs.120. Finally, the price of Hand-sanitizer is increased by 12%. If final price of the sanitizer is Rs.1120, then find the total percent increment in the price of sanitizer.​

Answer 1

SOLUTION

GIVEN

The price of Hand-sanitizer is first increased by 10%

Then increased by Rs.120.

Finally, the price of Hand-sanitizer is increased by 12%.

The final price of the sanitizer is Rs.1120

TO DETERMINE

The total percent increment in the price of sanitizer.

EVALUATION

Let initial price = Rs 100x

The price of Hand-sanitizer is first increased by 10%

First increase in price = Rs 10x

So the price of Hand-sanitizer after first increased of 10%

= Rs 100x + Rs 10x

= Rs 110x

Next the price increased by Rs. 120

After second increase the price is

= Rs ( 110x + 120 )

Next the price of Hand-sanitizer is increased by 12%

So final price of Hand-sanitizer

$\displaystyle \sf{ = Rs. \: \: (110x + 120) \times \frac{112}{100} }$

So by the given

$\displaystyle \sf{(110x + 120) \times \frac{112}{100} = 1120 }$

$\displaystyle \sf{ \implies \: (110x + 120) = 1120 \times \frac{100}{112} }$

$\displaystyle \sf{ \implies \: (110x + 120) = 1000 }$

$\displaystyle \sf{ \implies \: 110 x= 880}$

$\displaystyle \sf{ \implies \: x= 8}$

Initial price = Rs. ( 8 × 100 ) = Rs. 800

Final price = Rs. 1120

Total increase in price

= Rs. 1120 - Rs. 800

= Rs. 320

Hence the required total percent increment in the price of sanitizer

$\displaystyle \sf{ = \frac{320}{800} \times 100\% }$

$\displaystyle \sf{ = \frac{320}{8} \% }$

$\displaystyle \bf{ = 40 \% }$

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