Question

Example 4: Naresh sold two books for Rs. 600 each there by gaining 20% on one book and losing
20% on the other book. Find his over all loss or gain percent​

Answer 1

Given :-

• Naresh sold two books for Rs. 600 each there by gaining 20% on one book and losing 20% on the other book

To find :-

• Overall loss or gain percent

Solution :-

In first case

• Selling price of book (S.P) = Rs.600
• Gain percent on book (P%) = 20%

As we know that

→ Cost price = Selling price × 100/100 + Profit%

→ C.P = S.P × 100/100 + P%

→ C.P = 600 × 100/100 + 20

→ C.P = 60,000/120

→ C.P = 6,000/12

→ C.P = Rs.500

Hence,

• Cost price of book = Rs.500

In second case

• Selling price (S.P) = Rs.600
• Loss percent on book (L%) = 20%

As we know that

→ Cost price = Selling price × 100/100 - Loss%

→ C.P = S.P × 100/100 - 20

→ C.P = 600 × 100/80

→ C.P = 60,000/80

→ C.P = 6,000/8

→ C.P = Rs.750

Hence,

• Cost price of book = Rs.750

Now,

• Total selling price of book = 600 + 600 = Rs.1200
• Total cost price of book = 500 + 750 = 1250

→ Loss on book = Cost price - Selling price

→ Loss = 1250 - 1200

→ Loss = Rs.50

Now, overall loss percent

→ Loss% = Loss/C.P × 100

→ L% = 50/1250 × 100

→ L% = 50/125 × 10

→ L% = 4 %

Hence,

• Overall loss percent is 4%

Answer 2

☯ Given : Naresh sold two books for Rs. 600 each there by gaining 20% on one book and losing 20% on the other book.

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☯ Solution :

$\bullet\:\:\textsf{Selling price of first book = \textbf{600 Rs}}$

$\bullet\:\:\textsf{Profit = \textbf{20 \%}}$

$\underline{ \bigstar \: {\boldsymbol{According\: to \:the\: Question\:now :}} }</p><p>$

$:\implies\sf Cost \: price = \dfrac{100 \times SP}{ \big \{100 + profit \big \}}$

$:\implies\sf Cost \: price = \dfrac{100 \times 600}{ \big \{100 + 20 \big \}}$

$:\implies \underline { \boxed{\sf Cost \: price = 500 \: Rs}}$

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$\bullet\:\:\textsf{Selling price of second book = \textbf{600 Rs}}$

$\bullet\:\:\textsf{loss = \textbf{20 \%}}$

$\underline{ \bigstar \: {\boldsymbol{According\: to \:the\: Question\:now :}} }$

$:\implies\sf Cost \: price = \dfrac{100 \times SP}{ \big \{100 - loss \big \}}$

$:\implies\sf Cost \: price = \dfrac{100 \times 600}{ \big \{100 - 20\big \}}$

$:\implies \underline{ \boxed{\sf Cost \: price = 750 \: Rs}}$

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Therefore,

• Total cost price of two books = 500 + 750 = 1250 Rs.
• Total selling price of two books = 600 + 600 = 1200 Rs.

Here,

Selling price is more than cost price so loss :

$\dashrightarrow \sf Loss \: = \: cost \: price \: - \: selling \: price$

$\dashrightarrow \sf Loss \: = \: 1250 \: - \: 1200$

$\dashrightarrow \underline{ \boxed{\sf Loss \: = \: 50 \: Rs}}$

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Loss Percentage :

$\dashrightarrow \sf Loss \: \% \: = \dfrac{loss }{cost \: price} \: \times 100$

$\dashrightarrow \sf Loss \: \% \: = \dfrac{50 }{1250} \: \times 100$

$\dashrightarrow \underline{ \boxed{ \sf Loss \: \% \: = 4 \: \%}}$