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A fraction becomes 1/6 when 4 is subtracted from its numerator and 1 is added to its denominator. If 2 and 1 are respectively added to its numerator and the denominator, it becomes 1/3 Then, the LCM of the numerator and denominator of the said fraction, must be
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- 14
- 350
- 5
- 70
Correct Option: D
| Let the original fraction be | . | q |
| ∴ | = | q + 1 | 6 |
⇒ 6p – 24 = q + 1
⇒ 6p – q = 25 .......(i)
Again,
| ∴ | = | q + 1 | 3 |
⇒ 3p + 6 = q + 1
⇒ 3p – q = –5 .......(ii)
By equation (i) – (ii),
6p – q – 3p + q = 25 + 5
⇒ 3p = 30 ⇒ p = 10
From equation (i),
60 – q = 25 ⇒ q = 35
LCM of 10 and 35 = 70
