Question

A fraction becomes 1/2 when 10 is subtracted from its numerator and 25 is subtracted from its denominator. If 2 is multiplied its numerator and 5 is added to the denominator, it becomes 5/6. Find the LCM of the numerator and denominator of the fraction.
1. 255
2. 265
3. 285
4. 275

Answer 1

Correct Answer - Option 4 : 275

Calculation:

Let the numerator be x and denominator be y

According to condition,

\(\Rightarrow \frac{{x - 10}}{{y - 25}} = \;\frac{1}{2}\) 

⇒ 2x – 20 = y – 25

⇒ 2x – y = – 5      ----(1)

\(\Rightarrow \frac{{2x}}{{y + 5}} = \;\frac{5}{6}\) 

⇒ 12x = 5y + 25     ----(2)

From (1) × 6 – (2)

⇒ 12x – 6y – 12x = – 30 – 5y – 25

⇒ – y = – 55

⇒ y = 55

From (1)

⇒ 2x – 55 = – 5

⇒ 2x = 50

⇒ x = 25

⇒ Fraction will be = x/y = 25/55

∴ The LCM of the numerator (25) and denominator (55) of the fraction = 25 × 11 = 275.