Question

Given `1/(6x) - 1/(5y) = 1/60` and `1/(2x) + 1/y = 11/60`. Find (x, y).

Options

• (5, 12)

• (6, 10)

• (12, 5)

• (4, 8)

Answer 1

(5, 12)

Explanation:

Let `1/x = a` and `1/y = b`, then 

`1/6(a) - 1/5(b) = 1/60`

⇒ `a/6 - b/5 = 1/60`

`5a - 6b = 30/60 = 1/2`  ......(i)

`1/(2x) + 1/y = 11/60` ⇒ `a/2 + b = 11/60`

⇒ `a + 2b = 11/30`  ......(ii)

By equation (i) – (ii) × 5

`5a - 6b = 1/2`

`5a + 10b = 11/6`
–    –       –            
`- 16b = 1/2 - 11/6`

= `(3 - 11)/6 = (-8)/6 = (-4)/3`

⇒ `-16b = (-4)/3`

⇒ `b = 4/3 xx 1/16 = 1/12`

`b = 1/y = 1/12` ⇒ `y` = 12

From (ii),

`a + 2/12 = 11/30`

⇒ `a = 11/30 - 1/6 = 6/30 = 1/5`

∴ `a = 1/x = 1/5` ⇒ `x` = 5