# Word Problems on Profit and Loss

Math word problems on profit and loss will help us to review worked-out examples using the formula of profit and loss as a percentage of cost price/sale price.

Word Problems on Profit and Loss

1. By selling 33 m of carpet, a man loses an amount equal to the selling price of 3 m of carpet. Find his gain or loss per cent.

Solution:

Loss = (CP of 33 m) - (SP of 33 m)

⇒ (SP of 3 m) = (CP of 33 m) - (SP of 33 m)

⇒ (SP of 33 m) + (SP of 3 m) = (CP of 33 m)

⇒ (SP of 36 m) = (CP of 33 m).

Let the CP of 1 m be $x. Then, CP of 36 m =$ 36x

SP of 36m = (CP of 33m) = $33x. Thus, CP =$ 36x and SP = $33x. Since, (CP) > (SP), there is a loss. Loss =$ (36x - 33x) = $3x. Loss% = [(loss/CP) × 100]% = [(3x/36x) × 100] % = 25/3% = 8¹/₃% 2. Ronald buys a geyser for$ 3680 and sells it at a gain of 7¹/₂%. For how much does he sell it?

Solution:

CP of the geyser = $3680. Gain % = 7¹/₂% = 15/2%. Therefore, SP of the geyser = [{(100 + gain %)/100} × CP] =$ [{(100 + ¹⁵/₂)/100} × 3680]

= ${(215/200) × 3680} =$ 3956

Hence, Ronald sells the geyser for $3956. More solved examples for eighth grade math word problems on profit and loss formula for finding cost price and selling price. Word Problems on Profit and Loss 3. Jenny buys a calculator for$ 720 and sells it at a loss of 6²/₃)%. For how much does she sell it?

Solution:

CP of the calculator = $720. Loss % = 20/3% SP of the calculator = [{(100 - Loss %)/100} × CP] =$ [{(100 - 20/3)/100} × 720]

= ${(280/300) × 720} =$ 672

Hence, Jenny sells it for $672. 4. On selling of fan for$ 810, Sam gains 8%. For how much did he purchase it?

Solution:

SP of the fan = $810, gain % = 8%. Therefore, CP of the fan = {100/(100 + gain %) × SP} =$ {100/(100 + 8) × 810}

= ${(100/108) × 810} =$ 750

Hence, Sam purchased the fan for $750. 5. On selling a table for$ 987, Ron loses 6%. For how much did he purchase it?

Solution:

SP of the table = $987, loss % = 6%. Therefore, CP of the table = {100/(100 - loss %) × SP} =$ {100/(100 - 6) × 987}

= $(100/94) × 987 =$ 1050

Hence, Ron purchased the table for $1050. Practice word problems on profit and loss will help the students to review the questions to calculate profit % and loss % before solving the worksheet on profit and loss. 6. On selling a bat for$ 371, a man gains 6%. For how much should he sell it to gain 8%?

Solution:

SP of the bat = $371, gain % = 6%. Therefore, CP of the bat = {100/(100 + gain %) × SP} =$ {100/(100 + 6) × 371}

= ${(100/106) × 371} =$ 350

Now, CP = $350 and the desired gain% = 8%. Therefore, SP = [{(100 + gain %)/100} × CP] =$ [{(100 + 8)/100} × 350]

= ${(108/100) × 350} =$ 378

Hence, the selling price to obtain the desired gain is $378. 7. By selling a Jeans for$ 432, John loses 4%. For how much should John sell it to gain 6%?

Solution:

SP of the shirt = $432. Loss = 4% Therefore, CP of the shirt = {100/(100 - loss %) × SP} =$ {100 /(100 - 4) × 432}

= ${(100/96) × 432} =$ 450

Now, CP = $450, desired gain % = 6%. Desired SP = [{(100 + gain %)/100} × CP] =$ [{(100 + 6)/100} × 450]

= ${(106/100) × 450} =$ 477.

Hence, the desired selling price is \$ 477.

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