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Mathematics

Find the selling price :

(i) C.P. = ₹ 352, overheads = ₹ 28 and profit = 20%.

(ii) C.P. = ₹ 576, overheads = ₹ 44 and loss = 16%.

Profit, Loss & Discount

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Answer

(i) Given:

C.P. = ₹ 352

Overheads = ₹ 28

Hence, total C.P. = C.P. + overheads

= ₹ 352 + ₹ 28 = ₹ 380

Profit % = 20%

Profit %=ProfitC.P.×100\text{Profit \%} = \dfrac{\text{Profit}}{\text{C.P.}} \times \text{100}

Putting the values, we get

20=Profit380×100Profit=20×380100=7600100=76\Rightarrow20 = \dfrac{\text{Profit}}{380} \times 100\\[1em] \Rightarrow\text{Profit} = \dfrac{20 \times 380}{100} \\[1em] = \dfrac{7600}{100} \\[1em] = 76

As we know:

Profit=S.P. - C.P.76=S.P.380=380+76=456\text{Profit} = \text{S.P. - C.P.}\\[1em] \Rightarrow 76 = \text{S.P.} - 380\\[1em] = 380 + 76\\[1em] = 456

Hence, S.P. = ₹ 456.

(ii) Given:

C.P. = ₹ 576

Overheads = ₹ 44

Hence, total C.P. = C.P. + overheads

= ₹ 576 + ₹ 44 = ₹ 620

Loss % = 16%

Let the C.P. be ₹ xx.

Loss %=LossC.P.×100\text{Loss \%} = \dfrac{\text{Loss}}{\text{C.P.}} \times \text{100}

Putting the values, we get

16=Loss620×100Loss=16×620100=9,920100=99.2\Rightarrow16 = \dfrac{\text{Loss}}{620} \times 100\\[1em] \Rightarrow\text{Loss} = \dfrac{16 \times 620}{100} \\[1em] = \dfrac{9,920}{100} \\[1em] = 99.2

As we know:

Loss=C.P. - S.P.99.2=620S.P.S.P.=62099.2=520.80\text{Loss} = \text{C.P. - S.P.}\\[1em] \Rightarrow 99.2 = 620 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 620 - 99.2\\[1em] = 520.80

Hence, S.P. = ₹ 520.80.

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