Question

A man sold two of his scooters at Rs.22,000 each. On one he made a gain of 10% and on other he lost 12%.Find his overall loss or gain.

Answer 1

$\sf{\underline{\underline{ \purple{ \large{Given}}}}}$

✰ S.P of two scooters at Rs.22,000 each.

✰ Profit (gain)% on first scooter = 10%

✰ Loss% percent on first scooter = 12%

$\\ \\ \\ \sf{\underline{\underline{ \purple{ \large{To \: Find:}}}}}$

✠ Overall loss or gain.

$\\ \\ \\ \sf{\underline{\underline{ \purple{ \large{Solution:}}}}}$

Let there be two scooters X and Y

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For scooter X,

⇰Selling price ( S.P ) = Rs. 22,000

⇰Loss% = 10%

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Let's find out cost price ( C.P )

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Formula:

$\sf{ \purple{\star}}{ \blue{ \large{ \underline{ \boxed{ \sf{C.P. = \frac{100}{(100 + gain\%)} \times S.P.}}}}}}$

$\\ \\ \implies{\sf{C.P. = \frac{100}{(100 + 10)} \times 22000}}$

$\\ \\ \implies{\sf{C.P. = \frac{100}{110} \times 22000}}$

$\\ \\ \implies{\sf{C.P. = \frac{100}{11 \cancel0} \times 2200 \cancel0}}$

$\\ \\ \implies{\sf{C.P. = \frac{100}{ \cancel{11 }} \times \cancel{{2200}}^{200} }}$

$\\ \\ \implies{\sf{C.P. = 100 \times 200}}$

$\\ \\ \implies{\sf{C.P. = Rs. \: 20000}}$

Similarly, for Scooter Y

⇰Selling price ( S.P ) = Rs. 22,000

⇰Loss% = 12%

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Let's find out cost price ( C.P )

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Formula:

$\sf{ \purple{\star}}{ \blue{ \large{ \underline{ \boxed{ \sf{C.P. = \frac{100}{(100 - loss\%)} \times S.P.}}}}}}$

$\\ \\ \implies{\sf{C.P. = \frac{100}{(100 - 12)} \times 22000}}$

$\\ \\ \implies{\sf{C.P. = \frac{100}{88} \times 22000}}$

$\\ \\ \implies{\sf{C.P. = \frac{100}{ \cancel{88}} \times \cancel{{22000}}^{250} }}$

$\\ \\ \implies{\sf{C.P. = 100 \times 250}}$

$\\ \\ \implies{\sf{C.P. = Rs. \: 25000}}$

Now, let's find out total cost price and total selling price.

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• Total cost price = Rs. ( 20000 + 25000 )
• Total cost price = Rs. 45000

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• Total selling price = Rs. ( 22,000 + 22,000 )
• Total selling price = Rs. 44000

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As C.P. > S.P. profit has occurred,

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$\\ \sf{ \purple{ \large{ \star}{ \blue{ \large{ \underline{ \boxed{ \sf{Profit = S.P. - C.P.}}}}}}}}$

$\\ \\ \implies{ \sf{Profit =Rs. \: (45000 - 44000)}}$

$\\ \\ \implies{ \sf{Profit =Rs.1000}}$

$\sf{ \blue{ \therefore Profit \:accured} = { \green{ \large{ \underline{ \boxed{ \sf{Rs. \: 1000}}}}}}}$

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Answer 2

Answer:

$\sf{\underline{\underline{ \pink{ \large{Given}}}}}$

✰ S.P of two scooters at Rs.22,000 each.

✰ Profit (gain)% on first scooter = 10%

✰ Loss% percent on first scooter = 12%

$\\ \\ \\ \sf{\underline{\underline{ \pink{ \large{To \: Find:}}}}}$

✠ Overall loss or gain.

$\\ \\ \\ \sf{\underline{\underline{ \pink{ \large{Solution:}}}}}$

Let there be two scooters X and Y

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For scooter X,

⇰Selling price ( S.P ) = Rs. 22,000

⇰Loss% = 10%

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Let's find out cost price ( C.P )

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Formula:

$\sf{ \pink{\star}}{ \pink{ \large{ \underline{ \boxed{ \sf{C.P. = \frac{100}{(100 + gain\%)} \times S.P.}}}}}}$

$\\ \\ \implies{\sf{C.P. = \frac{100}{(100 + 10)} \times 22000}}$

$\\ \\ \implies{\sf{C.P. = \frac{100}{110} \times 22000}}$

$\\ \\ \implies{\sf{C.P. = \frac{100}{11 \cancel0} \times 2200 \cancel0}}$

$\\ \\ \implies{\sf{C.P. = \frac{100}{ \cancel{11 }} \times \cancel{{2200}}^{200} }}$

$\\ \\ \implies{\sf{C.P. = 100 \times 200}}$

$\\ \\ \implies{\sf{C.P. = Rs. \: 20000}}$

Similarly, for Scooter Y

⇰Selling price ( S.P ) = Rs. 22,000

⇰Loss% = 12%

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Let's find out cost price ( C.P )

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Formula:

$\sf{ \pink{\star}}{ \pink{ \large{ \underline{ \boxed{ \sf{C.P. = \frac{100}{(100 - loss\%)} \times S.P.}}}}}}$

$\\ \\ \implies{\sf{C.P. = \frac{100}{(100 - 12)} \times 22000}}$

$\\ \\ \implies{\sf{C.P. = \frac{100}{88} \times 22000}}$

$\\ \\ \implies{\sf{C.P. = \frac{100}{ \cancel{88}} \times \cancel{{22000}}^{250} }}$

$\\ \\ \implies{\sf{C.P. = 100 \times 250}}$

$\\ \\ \implies{\sf{C.P. = Rs. \: 25000}}$

Now, let's find out total cost price and total selling price.

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Total cost price = Rs. ( 20000 + 25000 )

Total cost price = Rs. 45000

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Total selling price = Rs. ( 22,000 + 22,000 )

Total selling price = Rs. 44000

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As C.P. > S.P. profit has occurred,

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$\\ \sf{ \pink{ \large{ \star}{ \pink{ \large{ \underline{ \boxed{ \sf{Profit = S.P. - C.P.}}}}}}}}$

$\\ \\ \implies{ \sf{Profit =Rs. \: (45000 - 44000)}}$

$\\ \\ \implies{ \sf{Profit =Rs.1000}}$

$\sf{ \pink{ \therefore Profit \:accured} = { \pink{ \large{ \underline{ \boxed{ \sf{Rs. \: 1000}}}}}}}$

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