Question

What is cost price if loss is 15% and selling price is Rs.2185? please include steps

Answer 1

Solution!!

The concept of profit and loss has to be used here. The loss percentage and the selling price (SP) is given. We have to find the cost price (CP).

Loss% = 15%

SP = Rs 2185

Loss% = ((CP - SP)/CP) × 100

15 = ((CP - Rs 2185)/CP) × 100

15 ÷ 100 = (CP - Rs 2185)/CP

0.15 = (CP - Rs 2185)/CP

0.15 CP = CP - Rs 2185

Rs 2185 = CP - 0.15 CP

Rs 2185 = 0.85 CP

CP ≈ Rs 2570.60

More information:-

• If SP>CP, then it is profit.

• If CP>SP, then it is loss.

• Loss = CP - SP

• Profit = SP - CP

• Loss% = (Loss/CP) × 100

• Profit% = (Profit/CP) × 100

Answer 2

Given :

• Selling Price (S.P) = Rs 2185
• Loss % = 15%

To Find :

• Cost Price (C.P)

Formula :

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

Solution :

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

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{100}{ \: 100 \: - \: 15} \: \times \: 2185 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{100}{ \: 85} \: \times \: 2185 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{100}{ \: \cancel{85}} \: \times \: \cancel{2185}} }$

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{100\: \times \: 437}{ \: 17} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{43700}{ \: 17} }}$

$\qquad \quad {:} \longrightarrow \sf \boxed{\bf{C.P \: = \: Rs \: 2570.58}}$

Thus Cost Price is Rs 2570.58

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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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