Question

The prices of two watches are in the ratio a:b. When the prices are both increased by Rs 10, the ratio becomes 5:7. When the prices are both reduced by Rs 10, the ratio becomes 1:3. Express the ratio a:b in its lowest terms.

Answer 1

Answer:

x : y = a : b = 3 : 5

Step-by-step explanation:

$\frac{x}{y} = \frac{a}{b}$

$\frac{x-10}{y-10} = \frac{1}{3}$

3x - 30 = y - 10

y = 3x - 20

$\frac{x+10}{y+10} = \frac{5}{7}$

7x + 70 = 5y + 50

7x + 20 = 5 (3x - 20)

7x + 20 = 15x - 100

8x = 120

x = 15

y = 3x - 20 = 45 - 20 = 25

∴ x : y = 15 : 25

∴ x : y = 3 : 5