Question

4. A rise of 25% in the price of an item compels a person to buy
of the item less for 240. Find the
increased price as well as the original price​

Answer 1

This is a ratio and proportions problem, with the ratio expressed as a unit rate: Price per weight or Rupees/kg

Old unit rate: 240 R

x kg the weight 'x' is unknown

New unit rate: 240 R times 25% increase = 300 R

x kg x kg

But, there are only 240 R to spend, so we take the new unit rate, and that is proportional to the lesser amount and the lower weight:

300 R = 240 R

x kg x - 1.5 kg Now cross multiply:

300 ( x - 1.5) = x times 240 Use distributive property to eliminate the parentheses:

300x - 450 = 240x

Isolate the variable x by subtracting 300x from both sides:

- 450 = - 60x Multiply both sides by -1:

and solve for x: x = 450/60 = 7.5 kg of sugar originally.

240 rupees/ 7.5 kg = 32 rupees/ kg and the new price is 32 * 1.25 =

40 rupees/kg

Answer 2

See the attached file

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