SOLUTION: 1. When a producer allows 36% commission on the retail price of his product, he earns a profit of 8.8%. What would be his profit percentage if the commission is reduced by 24%? 2.

Question 886762: 1. When a producer allows 36% commission on the retail price of his product, he earns a profit of 8.8%. What would be his profit percentage if the commission is reduced by 24%?
2. A and B start a business with invest of tk 5,000 and tk 4,500 respectively. After 4 months, A takes out half of his capital. After 2 more months, B takes out one third of his capital while C joints them with a capital of tk 7,000. At the end of a year, they earn a profit of tk 5,080. Find the share of each member in the profit.
3. 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1 boy do the work?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
1. When a producer allows 36% commission on the retail price of his product, he earns a profit of 8.8%. What would be his profit percentage if the commission is reduced by 24%?

let x = selling price.
he pays 36% commission so he nets .64*x
he makes 8.8% profit on that, so his cost has to be .64*x / 1.088 = .5882352941*x

now he reduces his commission by 24%.
this means the commission is now 12% instead of 36%.
he now nets .88*x
since his cost remains the same at .5882352941*x, then his profit becomes .88*x / .5882352941*x = 1.496.

he will earn 49.6% profit.

let's put this in numbers to see how it pans out.

he sells the product for $200.00
he now has to pay out 36% commission on that, so he nets $200.00 minus .36 * $200 which is equal to $128.

he makes a profit of 8.8% on $128, so his cost had to be $128 / 1.088 = 117.6470588

now he takes the product that sells for $200 and reduces the commission by 24% which mean the commission is now 12%.

he nets .88 * 200 = 176 dollars.
his cost remains the same at 117.6470588.
his new profit is equal to (176 - 117.6470588)/117.6470588 = .496
he gets 49.6% profits instead of 8.8% by reducing the commission from 36% to 12%.
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2. A and B start a business with invest of tk 5,000 and tk 4,500 respectively. After 4 months, A takes out half of his capital. After 2 more months, B takes out one third of his capital while C joints them with a capital of tk 7,000. At the end of a year, they earn a profit of tk 5,080. Find the share of each member in the profit.

this really depends on what agreement they made up front as to how the money would be split.

a reasonable split would be based on total dollar months invested.

A invests 5000 for 4 months and 2500 for 8 months for a total of 40000.
B invests 4500 for 6 months and 3000 for 6 months for a total of 45000.
C invest 7000 for 6 months for a total of 42000.

the total dollar months invested is equal to 127000

A owns 40/127 of that.
B owns 45/127 of that.
C owns 42/127 of that.

they would split the profit by those ratios.
the profit is 5080.

A gets 40/127 * 5080 = 1600.
B gets 45/127 * 5080 = 1800.
C gets 42/127 * 5080 = 1680.

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3. 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1 boy do the work?

rate * time = quantity of work.l
let m = rate of the one an
let b = rate of 1 boy.

you get the following equations:

(2m + 3b) * 10 = 1
(3m + 2b) * 8 = 1

simplify these to get:

20m + 30b = 1
24m + 16b = 1

solve these equations simultaneously to get b = 1/100 and m = 7/200.

those are your solutions.

plug those solutions back into the original equations and you will see that they are confirmed as correct.

(2 * 7/200 + 3 * 1/100) * 10 = 1
(3 * 7/200 + 2 * 1/100) * 8 = 1

you can now use these rates to solve the problem.

(2m + 1b) * x = 1 becomes:
2 * 7/200 + 1 * 1/100) * x = 1
simplify to get:
(14/200 + 1/100) * x = 1
simplify further to get:
16/200 * x = 1
divide both sides of this equation by 16/200 to get:
x = 1 * 200/16 = 12.5 days.

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