Question 1081193: 1.) Dele lost 18% by selling bicycle for #1,230. What percent shall he gain by selling it for #1,600?
2.) A shop keeper sells an article at a gain of 10%. Had he sold it at a loss of 20%, it's selling price would have been #180 less. What is the cost price of the article?
3.) A person sells a colour TV at 10% below cost price. Had he received #1,494
more, he would have made a profit of 12 1/2% (12 & half percent). What was the cost price of colour TV?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 1.) Dele lost 18% by selling bicycle for #1,230. What percent shall he gain by selling it for #1,600?
let x equal the cost.
he sold it for 1230 at a loss of 18%.
x - .18 * x = .88 * x
.82 * x = 1230
solve for x to get x = 1230/.82 = 1500
his cost was 1500.
if he had sold it for 1600 rather than 1230, he would have made a gain of 100 over his cost of 1500.
100/1500 = 1/15 = .066666666..... * 100 = 6.666666..... percent.
this is equivalent to 6 and 2/3 percent.
the cost is 1500.
he sell is for a n 18% loss which means he sells it for .82 * 1500 = 1230.
if he had sold it for a profit of 6 and 2/3 %, he would have sold it for 1500 * (1 + 2/3) % / 100 which would have been equal to 1600
solution look good.
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2.) A shop keeper sells an article at a gain of 10%. Had he sold it at a loss of 20%, it's selling price would have been #180 less. What is the cost price of the article?
let x = the cost.
if he sold it at 10% profit, then the selling price was 1.10 * x.
if he sold it at 20% loss, then the selling price was .80 * x.
if he sold it at a loss of 20%, his selling price would have been 180 less than if he sold it at 10% profit.
.80 * x = 1.10 * x - 180
add 180 to both sides of this equation and subtract .80 * x from both sides of this equation to get:
180 = 1.10 * x - .80 * x
combine like terms to get .30 * x = 180
solve for x to get x = 180 / .30 = 600
the cost was 600.
if he sold it at 10% profit, the selling price would have been 660.
if he sold it at 20% loss, the selling price would have been 480
the difference is 660 - 480 = 180
solution looks good.
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3.) A person sells a color TV at 10% below cost price. Had he received #1,494 more, he would have made a profit of 12 1/2% (12 & half percent). What was the cost price of color TV?
let x = the cost.
he sells it at a loss of 10%, therefore the selling price is .90 * x.
if he had received 1494 more, he would have made a profit of 12 and 1/2 %.
12 and 1/2 % is equal to 12.5 percent / 100 is equal to .125.
his profit would have been 12.5% which means he would have sold it for 1.125 * cost.
his selling price would therefore have been 1.125 * x.
.90 * x + 1494 = 1.125 * x
subtract .90 * x from both sides of the equation to get:
1494 = 1.125 * x - .90 * x
combine like terms to get:
1494 = .225 * x
solve for x to get x = 1494 / .225 =
the cost would have been 6640.
he sold it at a 10% loss which means he sold it for .9 * 6640 = 5976
if he had sold it for 1494 more, he would have made a profit of 12.5%
5976 + 1494 = 7470
7470 / 6400 = 1.125
(1.125 - 1) * 100 = 12.5%.
solution looks good.
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