Question

By selling a watch for ₹1830, Rahul made a profit of 20%. Find the cost price of the watch.​

Answer 1

Answer :

• 1525

Given :

• The selling price of a watch and the profit percentage.

To Find :

• The Cost Price of the watch.

Let's start :

Here,

• SP = Rs 1830

Percentage of profit = 20%

or, P = 20

Solution :

$\therefore \rm CP = \frac{100}{100 \: + \: profit} \times \: SP \\ \\ = \rm \frac{100}{100 \: + \: 20} \times \: 1830 \\ \\ = \frac{100}{120} \times \: 1830 \\ \\ = \large \bf1525$

Therefore, Cost price of the watch = 1525

More knowledge :

• Cost price : This is the price at which anything is purchased.

• Selling price : This is the price at which anything is sold.

• Profit : If the selling price is more than the cost price, then there is profit.

• Loss : If the cost price is more than the selling price, then there is loss.

Formulae :

• Profit = the selling price - cost price.

• Loss = cost price - selling price.

Answer 2

Given :

• Selling Price (S.P) = Rs 1830
• Profit % = 20%

To Find :

• Cost Price of Watch

Formula :

$\blue \bigstar \: {\underline{\boxed {\mathcal{\pmb{ \red{\quad C.P \: = \: \dfrac{100}{ \: 100 \: + \: Gain\%} \: \times \: S.P}\quad}}}}}$

Solution :

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{100}{ \: 100 \: + \: Gain\%} \: \times \: S.P }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{100}{ \: 100 \: + \: 20} \: \times \: 1830 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{100}{ \: 120} \: \times \: 1830 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{100}{ \: 12\cancel{0}} \: \times \:183 \cancel{0}} }$

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{100\: \times \: 183}{ \: 12} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{18300}{ \: 12} }}$

$\qquad \quad {:} \longrightarrow \sf \boxed{\bf{C.P \: = \: Rs \: 1525}}$

Thus Cost Price of Watch is Rs 1525

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$\small\boxed{ \begin{array}{cc}\large\sf\dag \: {\underline{More \: Formulae}} \\ \\ \bigstar \: \sf{Gain = S.P – C.P} \\ \\ \bigstar \:\sf{Loss = C.P – S.P} \\ \\ \bigstar \: \sf{Gain \: \% = \Bigg( \dfrac{Gain}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{loss \: \% = \Bigg( \dfrac{loss}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{S.P = \dfrac{100+Gain\%}{100} \times C.P} \\ \\ \bigstar \: \sf{ C.P =\dfrac{100}{100+Gain\%} \times S.P} \\ \\\bigstar \: \sf{ S.P = \dfrac{100-loss\%}{100} \times C.P} \\ \\ \bigstar \: \sf{ C.P =\dfrac{100}{100-loss\%} \times S.P}\end{array} }$

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