Problema Solution
1. A man sold a radio to his friend at a discount of 40%. Find the percentage gain or loss if his usual profit, without discount, was 50%.
2. A man bought some eggs at x cents each. y of them were broken while the rest of them were sold at z cents each. If he made a total profit of w cents, find the number of eggs he bought in terms of x, y, z, and w.
3. Alan bought a piece of land and sold it to Bill at a profit of 10 percent. Later on, Bill sold it back to Alan at a profit of 10%. What percentage would Alan had saved on the cost of the piece of land had he not sold it to Bill? Give the answer correct to 2 decimal places.
Answer provided by our tutors
1.
let x = the cost price
the regular sell price is: x + 0.50x = 1.50x (since it earns 50% profit)
the discounted sell price is the regular sell price - 40% discount that is 1.5x - 0.40*1.50x = 0.60*1.50x = 0.90x
the gain/loss of profit is: 0.90 - x = -0.10x
the percentage of loss is 10%
2.
let t = total number of eggs bought
x = original cost per eggs
tx = the total cost for x eggs
(t-y) = number of eggs sold (since y were broken)
z(t-y) = amount he got by selling (t - y) eggs for z cents each
total profit: z(t-y) - tx = w
zt - zy - tx = w
t(z - x) = w - zy
t = (w - zy)/(z - x)
3.
let x = the original sell price that Alan paid for the land
Alan bought a piece of land and sold it to Bill at a profit of 10 percent: this means Alan sold it for x + 0.10x = 1.10x
Later on, Bill sold it back to Alan at a profit of 10%: this means Bill sold it for 1.10x + 0.10*1.10x = 1.10*1.10x = ((1.10)^2)x
the percentage of loss is: (((1.10)^2)x - x)/x = (1.10)^2 - 1 = 0.21 or 21%
If Alan didn't sell the land he would have saved 21%.