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The difference between two selling prices of a shirt at profits of $4 %$ and $5 %$ is Rs. 6. Find, the two selling prices of the shirt.

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Rs. 624, Rs.630

Rs. 624, Rs.680

Rs. 654, Rs.630

Rs. 524, Rs.630

answer is A.

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Detailed Solution

Given,
For shirt 1 profit is 4%,
For shirt 2 profit is 5%.
Let the cost price (CP) of both the shirts be Rs.x.
For shirt one profit is 4%.
The formula for profit percentage is,

Profit % = profit CP (100)

4 = Profit C P (100) ⇒ Profit = 4100 CP ⇒ Profit = 0 .04 x

Now, selling price (SP) is,

SP = CP + profit

⇒ x + 0.04 x ⇒ 1.04 x

For shirt, the second profit is 5%.

CP = Rs x ⇒ Profit % = Profit CP (100) ⇒ Profit = 5100 CP ⇒ Profit = Rs .0.05 x Now, SP = CP + profit ⇒ x + 0.05 x ⇒ 1.05 x

It is given that the difference between their profits is 6.
Therefore, taking difference of both the selling price,

1.05 x − 1.04 x = 6 0.01 x = 6 x = 600

Calculating selling price of first shirt,

⇒ SP for first shirt = 1.04 x ⇒ 1.04 600 ⇒ 624

Calculating selling price of second shirt,

⇒ SP for second shirt = 1.05 x ⇒ 1.045 600 ⇒ 630

Thus, the selling price of shirts are Rs.624 and Rs.630.
Therefore, option (1) is correct.

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