A man purchases two table lamps for rs 2430. By selling one table lamp at a profit of 6% and the other at a loss of 3% he neither gains nor losses on this transaction . Find the cost price of each lamp

Open in App

Solution

$Let the CP of first table lamp = Rs x Then the CP of second table lamp = Rs (2430 - x) Profit on selling first lamp = 6 % Profit % = [\frac{Profit}{CP} \times 100] % \Rightarrow 6 = (\frac{Profit}{x} \times 100) \Rightarrow 50 profit = 3 x \Rightarrow 50 (SP - CP) = 3 x \Rightarrow 50 (SP - x) = 3 x \Rightarrow SP = Rs (\frac{53 x}{50}) Loss on selling second lamp = 3 % loss % = [\frac{loss}{CP} \times 100] % \Rightarrow 3 = (\frac{loss}{2430 - x} \times 100) \Rightarrow 100 loss = 7290 - 3 x \Rightarrow 100 (CP - SP) = 7290 - 3 x \Rightarrow 100 (2430 - x - SP) = 7290 - 3 x \Rightarrow SP = Rs (\frac{235710 - 97 x}{100}) Total SP of both lamps = (\frac{53 x}{50}) + (\frac{235710 - 97 x}{100}) = Rs (\frac{9 x + 235710}{100}) Total CP of both lamps = Rs 2430 Since there is neither gain nor loss inthe transaction, so Total SP of both lamps = Total CP of both lamps \Rightarrow \frac{9 x + 235710}{100} = 2430 \Rightarrow 9 x + 235710 = 243000 \Rightarrow 9 x = 7290 \Rightarrow x = 810 So, CP of first lamp = Rs 810 CP of second lamp = 2430 - 810 = Rs 1620$

Suggest Corrections

Similar questions

A man purchases two fans for $R s . 2160.$ By selling one fan at a profit of $15 %$ and the other at a loss of $9 %$ he neither gains nor losses in the whole transaction. Find the cost price of each fan.

Q. A man purchases two pens for Rs.

740.

He sells one at

12 %

profit and the other at

8 %

loss. Then he neither gains nor loses. Find the cost price (in Rs.) of each pen.

Q. A man sells a handset for Rs

5600

and incurs a loss of

20 %

. He sells a second handset at a profit of

50 %

. If on the whole transaction, he neither gains nor less, find the cost price of the second handset.

Q. A man buys two cycles for a total cost of

R s . 900

. By selling one cycle at a loss of

20 %

and the other at a profit of

25 %

, he makes a profit of

R s . 90

on the whole transaction. Find the cost price of each cycle.

Q. I bought two tables for Rs.

5400

. I sold one at a loss of

5 %

and the other at a gain of

7 %

. In the whole transaction, I neither gained nor lost. Find the costs of the tables separately.

Join BYJU'S Learning Program