Question

the ratio of price of geometry box to the calculator is 3:4 .the total price of both is rs 350 . if the prices of geometry box and calculator are increased by 1/3 and 1/5 respectively of their original prices, find the ratio of increased price of the calculator to the price of the geometry box.

Answer 1

Ratio of geometry box : calculator = 3 : 4 (given)

Define x:

Let x be the constant ratio

Ratio of geometry box : calculator = 3x : 4x

Given that the total price is Rs 350:

3x + 4x = 350

7x = 350

x = 350 ÷ 7 = Rs 50

Find the price of the items:

Geometry set = 3x = 3(50) = Rs 150

Calculator = 4x = 4(50) = Rs 200

Find the new price:

Geometry set : increase in price = 1/3 x 150 = Rs 50

Geometry set : new price = 150 +  50 = Rs 200

Calculator - increase in price = 1/5 x 200 = Rs 40

Calculator - new price = 200 + 40 = Rs 240

Find the new ratio:

Ratio of geometry box : calculator = 200 : 240

Simplify by dividing by 40:

Ratio of geometry box : calculator = 5 : 6

Answer: The new ratio is 5:6

Answer 2

given ratio = 3:4

let geometry cost = 3x

and calculator cost = 4x

given total cost = 350.

3x + 4x = 350

7x = 350

x = 350/7 = 50.

geometry price = 3(50) = 150

calculator price = 4(50) = 200 .

increase in price --

geometry price = 150 x 1/3 = 50

= 150 + 50 = 200 .

geometry new price = 200

calculator price = 200 x 1/5 = 40

= 200 + 40 = 240

calculator new price = 240

finding ratio of new prices --

geometry : calculator

200 : 240

20 : 24

5 : 6.

hence required answer is 5 : 6