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Mathematics

A tape recorder is sold for ₹ 2,760 at a gain of 15% and a C.D. player is sold for ₹ 3,240 at a loss of 10%. Find

(i) the C.P. of the tape recorder.

(ii) the C.P. of the C.D. player.

(iii) the total C.P. of both.

(iv) the total S.P. of both.

(v) the gain % or the loss% on the whole.

Profit, Loss & Discount

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Answer

(i) Given:

S.P. of tape recorder = ₹ 2,760

Gain% on one tape recorder = 15%

Let C.P. of tape recorder = ₹ xx.

As we know,

Gain%=GainC.P.×100⇒15=Gainx×100⇒Gain=15×x100⇒Gain=3x20\text{Gain\%} = \dfrac{\text{Gain}}{\text{C.P.}} \times 100\\[1em] \Rightarrow15 = \dfrac{\text{Gain}}{x} \times 100\\[1em] \Rightarrow\text{Gain} = \dfrac{15 \times x}{100}\\[1em] \Rightarrow\text{Gain} = \dfrac{3x}{20}

And,

Gain = S.P. - C.P.⇒3x20=2,760−x⇒3x20+x=2,760⇒3x20+20x20=2,760⇒(3x+20x)20=2,760⇒23x20=2,760⇒x=2,760×2023⇒x=55,20023⇒x=2,400\text{Gain = S.P. - C.P.}\\[1em] \Rightarrow\dfrac{3x}{20} = 2,760 - x\\[1em] \Rightarrow\dfrac{3x}{20} + x = 2,760\\[1em] \Rightarrow\dfrac{3x}{20} + \dfrac{20x}{20} = 2,760\\[1em] \Rightarrow\dfrac{(3x + 20x)}{20} = 2,760\\[1em] \Rightarrow\dfrac{23x}{20} = 2,760\\[1em] \Rightarrow x = \dfrac{2,760\times20}{23}\\[1em] \Rightarrow x = \dfrac{55,200}{23}\\[1em] \Rightarrow x = 2,400

Hence, the cost price of tape recorder = ₹ 2,400.

(ii) Given:

S.P. of the CD Player = ₹ 3,240

Loss% = 10%

Let the C.P. of the CD Player be ₹ xx

As we know,

Loss%=LossC.P.×100⇒10=Lossx×100⇒Loss=10×x100⇒Loss=x10\text{Loss\%} = \dfrac{\text{Loss}}{\text{C.P.}} \times 100\\[1em] \Rightarrow10 = \dfrac{\text{Loss}}{x} \times 100\\[1em] \Rightarrow\text{Loss} = \dfrac{10 \times x}{100}\\[1em] \Rightarrow\text{Loss} = \dfrac{x}{10}

And,

Loss = C.P. - S.P.⇒x10=x−3,240⇒x−x10=3,240⇒10x10−x10=3,240⇒(10x−x)10=3,240⇒9x10=3,240⇒x=3,240×109⇒x=32,4009⇒x=3,600\text{Loss = C.P. - S.P.}\\[1em] \Rightarrow\dfrac{x}{10} = x - 3,240\\[1em] \Rightarrow x - \dfrac{x}{10} = 3,240\\[1em] \Rightarrow\dfrac{10x}{10} - \dfrac{x}{10} = 3,240\\[1em] \Rightarrow\dfrac{(10x - x)}{10} = 3,240\\[1em] \Rightarrow\dfrac{9x}{10} = 3,240\\[1em] \Rightarrow x = \dfrac{3,240 \times10}{9}\\[1em] \Rightarrow x = \dfrac{32,400}{9}\\[1em] \Rightarrow x = 3,600

Hence, the cost price of CD Player = ₹ 3,600.

(iii) Total C.P. of both = ₹ 2,400 + ₹ 3,600

= ₹ 6,000

Total C.P. of both items = ₹ 6,000

(iv) Total S.P. of both = ₹ 2,760 + ₹ 3,240

= ₹ 6,000

Total S.P. of both items = ₹ 6,000

(v) As S.P. is equal to C.P., means article is sold at neither loss nor gain.

Hence, the overall gain percent or loss percent = 0%.

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