If 9685 is divided into three parts in such a way that one-fourth of the first part, one-third of the second part and one sixth of the third part are equal, then what is the first part?

2980

According to the question,

⇒ a + b + c = 9685

\(\frac{1}{4}\)a = \(\frac{1}{3}\)b = \(\frac{1}{6}\)c

⇒ Taking LCM 12

⇒ 3a = 4b = 2c

⇒ Taking LCM 12

⇒ a : b : c = 4 : 3 : 6

⇒ (4 + 3 + 6) units = 9685

⇒ 13 units = 9685

⇒ 1 unit = 745

⇒ First part = 4 x 745 = 2980.