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At a railway station, a tooth seller bought few datuns (wooden toothbrush) at the rate of 6 per Rs. 100. Second time he bought he same number of datuns at rate of 5 per Rs. 100. He mixed both the lots and then sold the datuns at the rate o7  per Rs. 200. In this business he had a loss of Rs. 1320.What are the number of datuns he bought ?

At a railway station, a tooth seller bought few datuns (wooden toothbrush) at the rate of 6 per Rs. 100. Second time he bought he same number of datuns at rate of 5 per Rs. 100. He mixed both the lots and then sold the datuns at the rate o7  per Rs. 200. In this business he had a loss of Rs. 1320.What are the number of datuns he bought ? Correct Answer 168

Given∶

He bought few datuns at the rate of 6 per Rs. 100.

Second time he bought he same number of datuns at rate of 5 per Rs. 100.

He mixed both the lots and then sold the datuns at the rate of 7 per Rs. 200.

He had a loss of Rs. 1320.

Formula Used∶

Basics of Profit & Loss and Unitary Method.

S.P. = C.P. - Loss

Calculation∶

Let the number of datuns he bought on each occasion be 'x'.

For the 1st transaction, he bought x datuns paying Rs. 100 for 6.

Applying unitary method to find the total cost of x number of datuns.

He bought first time x datuns for Rs. 100

So, his cost per datun = 100/6

and, for x numbers of datuns, total cost = 100x/6

Similarly for 2nd purchase,

Total cost for x number of datuns = 100x/5

For 2x number of datuns, his totalcost, C.P. = 100x/6 + 100x/5 = 1100x/30

He sold it athe rate of 7 for Rs. 200, that is at a sale price per datun = Rs. 200/7

For 2x number of datuns, S.P. = Rs. 400x/7

Also, S.P. = C.P. - Loss

⇒ 400x/7 = 1100x/30 - 1320

⇒ 330x = 1320 × 21

⇒ x = 84

⇒ 2x = 2 × 84 = 168

∴ Total number of datuns he bought was168.

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