Question

A sells an item to B at a profit of 1/5 of its cost. B sells it to C at a profit of 20%. Accordingly, if C Sell ​​it for ₹ 600 and he has lost 1/6 of his cost, what is the cost price of A?​

Answer 1

Answer:

$\underline{\bigstar\:\:\textsf{Cost Price for C :}}$

$:\implies\sf SP = CP \times (1 - Loss)\\\\\\:\implies\sf 600=CP \times \bigg(1 - \dfrac{1}{6}\bigg)\\\\\\:\implies\sf 600=CP \times \bigg(\dfrac{6 - 1}{6}\bigg)\\\\\\:\implies\sf 600 = CP \times \dfrac{5}{6}\\\\\\:\implies\sf 600 \times \dfrac{6}{5} = CP\\\\\\:\implies\sf 120 \times 6 = CP\\\\\\:\implies\sf CP = 720$

$\rule{150}{1}$

$\underline{\bigstar\:\:\textsf{According to the Question :}}$

$\dashrightarrow\sf\:\:A's\:CP \times (1+Profit) \times (100+Profit)\%=C's\:CP\\\\\\\dashrightarrow\sf\:\:A's\:CP \times\bigg(1 + \dfrac{1}{5} \bigg) \times (100 + 20)\% = 720\\\\\\\dashrightarrow\sf\:\:A's\:CP \times \dfrac{6}{5} \times 120\% = 720\\\\\\\dashrightarrow\sf\:\:A's\:CP \times \dfrac{1}{5} \times \dfrac{120}{100} = 120\\\\\\\dashrightarrow\sf\:\:A's\:CP \times \dfrac{1}{5} \times \dfrac{1}{100} = 1\\\\\\\dashrightarrow\:\:\underline{\boxed{\sf A's\:CP = Rs. \:500}}$

⠀

$\therefore\:\underline{\textsf{Cost Price for A will be \textbf{Rs. 500}}}.$

Answer 2

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$\huge\tt{SOLUTION:}$

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Cost Price of C :

↪SP=CP×(1-LOSS)

↪600=CP×6-1/6

↪600=CP×5/6

↪600×6/5=CP

↪120×6=CP

↪₹720=CP

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Accordingly to the question,

➡A's CP × (1+profit)×(100+profit)% = C's CP

➡A's CP ×(1+¹/5)×(100+20%)=720

➡A's CP × 6/5 × 120% = 720

➡A's CP × 1/5 × 120/100 = 120

➡A's CP × 1/5 × 6/5 = 120

➡A's CP × 6/25 = 120

➡A's CP × 6 = 120×25

➡A's CP = 120×25/6

➡A's CP = 20× 25

➡A's CP = ₹500

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