Question

a press was sold at a loss of 8 % . Had it been sold for Rs 56 more , there would have been a profit of 8 % . What was the cost price of the press ​

Answer 1

Gɪᴠᴇɴ :-

• Initial Loss % of Press = 8% .
• Increased SP = Rs.56
• New Profit = 8% .

Tᴏ Fɪɴᴅ :-

• Cost Price of Press ?

Sᴏʟᴜᴛɪᴏɴ :-

Let us Assume That, Cost Price of Press is Rs.100X.

Case 1) :-

→ CP = 100x .

→ Loss = 8% .

→ SP = [CP * (100 - Loss%) ] / 100

→ SP = [ 100x * (100 - 8) ] / 100

→ SP = (100x * 92) / 100

→ SP = 92x .

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Case 2) :-

→ New SP = Old SP + Rs.56

→ New SP = (92x + 56)

→ New Profit = 8% .

So,

→ CP = (SP * 100) / (100 + Profit%) .

→ CP = [(92x+56) * 100 ] / (100 + 8)

→ CP = (9200x + 5600) / 108

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Comparing With Our Assume CP now, we get,

→ 100x = (9200x + 5600) / 108

→ 100x * 108 = 9200x + 5600

→ 10800x = 9200x + 5600

→ 10800x - 9200x = 5600

→ 1600x = 5600

→ x = 3.5.

Hence,

→ Original CP of Press = 100x = 100 * 3.5 = Rs.350 (Ans.)

Therefore , Cost Price of Press was Rs.350.

Answer 2

Aɴꜱᴡᴇʀ

☞ C.P = Rs 350

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Gɪᴠᴇɴ

✴ At the beginning the press lost 8%

✴ If the S.P was increased by Rs 54 then the new profit is 8%

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ᴛᴏ ꜰɪɴᴅ

✪ The C.P of the press

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Sᴛᴇᴘꜱ

❍ So let's assume that the C.P of the Press is 100x

➜ So with the given information,we can find the S.P

$\large \tt \mapsto \red{s.p = \frac{c.p(100 - loss)}{100} } \\ \\ \large \tt \leadsto{} \frac{100x(100 - 8)}{100} \\ \\ \large \tt \leadsto \frac{ \cancel{100}x(92)}{ \cancel{100}} \\ \\ \large \leadsto \tt{s.p = 92x}$

❍ So now the new S.P is,

$\large \implies{} \tt{}new \: \: s.p = old \: s.p + 56 \\ \\ \large \tt \implies92x + 56$

❍ So then the C.P is equal to,

$\large \mapsto{ \red{ \tt{}c.p = \frac{s.p \times 100}{100 + profit} }} \\ \\ \large \tt \longrightarrow{} \frac{(92x + 56) \times 100}{100 + 8} \\ \\ \large \tt \longrightarrow \frac{9200x + 5600}{108}$

➜ Equating it with our assumed C.P

$\large \tt \dashrightarrow{}100x = \frac{9200x + 5600}{108} \\ \\ \large \tt \dashrightarrow100x \times 108 =9200x + 5600 \\ \\ \large \tt \dashrightarrow10800x - 9200x = 5600 \\ \\ \large \tt \dashrightarrow1600x = 5600 \\ \\ \large \tt \dashrightarrow{}x = \cancel\frac{ 5600}{1600} \\ \\ \large \tt \dashrightarrow{\pink{x = 3.5}}$

So that now we have the value of X let's find the C.P of the press by,

$\large \tt \leadsto{}c.p = 100 \times 3.5 \\ \\ \tt \large \pink{\leadsto{}c.p =Rs \: 350}$

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