Question

iling price is the profit?
Joy 10%, but the selling price remains
8. A mechanic sells two machines for 15,000 each. On one, he gains 25% and on the other, he loses
25%. What is his total loss or gain percent?
shopkeeper increases the price of his goods​

Answer 1

➤ Correct Question :-

A mechanic sells two machines for ₹15,000 each. On one, he gains 25% and on the other, he loses 25%. What is his total loss or gain percent?

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➤ Given :-

Selling price of each machine :- ₹15000

Gain percent of first machine :- 25%

Loss percent of second machine :- 25%

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➤ To Find :-

The profit or loss percentage of whole transaction...

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★ How to do :-

Here, we are given with that a mechanic sells two machines at a same price. But, he occurs some gain and loss percentage in his machines while selling those. Although the selling price of both machines are same, there are different gain and loss percent on both of the machines. As this is the given information, the cost price of both the machines are different. We are asked to find the total gain or loss percent that will obtain to the mechanic while he sells those both machines. So, first we should find the cost prices of both the machines separately. Then, we can find the profit or loss by subtracting the cost and selling prices of those machines. Then, we use the formula of the gain or loss percentage and then, we can get our answer. So, let's solve!!

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➤ Solution :-

Cost price of first machine :-

${\sf \longrightarrow \underline{\boxed{\sf \dfrac{100}{100 + Gain \%} \times SP}}}$

Substitute the given values.

${\sf \leadsto \dfrac{100}{100 + 25} \times 15000}$

Write the fraction in lowest form by cancellation method.

${\sf \leadsto \cancel \dfrac{100}{125} \times 15000 = \dfrac{4}{5} \times 15000}$

Multiply the remaining numbers.

${\sf \leadsto \dfrac{4 \times 15000}{5} = \dfrac{60000}{5}}$

Write the fraction in lowest form by cancellation method.

${\sf \leadsto \cancel \dfrac{60000}{5} = 12000}$

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Cost price of second machine :-

${\sf \longrightarrow \underline{\boxed{\sf \dfrac{100}{100 - Loss\%} \times SP}}}$

Substitute the given values.

${\sf \leadsto \dfrac{100}{100 - 25} \times 15000}$

Write the fraction in lowest form by cancellation method.

${\sf \leadsto \cancel \dfrac{100}{75} \times 15000 = \dfrac{4}{3} \times 15000}$

Multiply the remaining numbers.

${\sf \leadsto \dfrac{4 \times 15000}{3} = \dfrac{60000}{3}}$

Write the fraction in lowest form by cancellation method.

${\sf \leadsto \cancel \dfrac{60000}{3} = 20000}$

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Now, let's solve the total cost price and the total selling price.

Total cost price :-

${\sf \leadsto 12000 + 20000}$

Add the values.

${\sf \leadsto 32000}$

Total selling price :-

${\sf \leadsto 15000 + 15000}$

Add the values.

${\sf \leadsto 30000}$

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Loss rupees :-

${\sf \leadsto 32000 - 30000}$

Subtract the values.

${\sf \leadsto 2000}$

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Now, let's find the loss percentage on the whole transaction.

Loss percentage :-

${\sf \longrightarrow \underline{\boxed{\sf \dfrac{Loss}{Cost \: price} \times 100}}}$

Substitute the given values.

${\sf \leadsto \dfrac{2000}{32000} \times 100}$

Write the fraction in lowest form by cancellation method.

${\sf \leadsto \cancel \dfrac{2000}{32000} \times 100 = \dfrac{1}{16} \times 100}$

Multiply the remaining numbers.

${\sf \leadsto \dfrac{1 \times 100}{16} = \dfrac{100}{16}}$

Write the fraction in lowest form by cancellation method.

${\sf \leadsto \cancel \dfrac{100}{16} = 6.25}$

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${\red{\underline{\boxed{\bf So, \: the \: loss \: percentage \: on \: whole \: transaction \: is \: 6.25\%.}}}}$