Concept: $(\FRAC{1}{a}:\frac{1}{b}:\frac{1}{c} = \frac{{LCM\;of\;\left( {a,b,c} \right)}}{a}:\frac{{LCM\;of\;\left( {a,b,c} \right)}}{b}:\frac{{\left( {LCM\;of\;\left( {a,b,c} \right)} \right)}}{c})$

GIVEN,

A can do a PIECE of work in 12 days.

∴ Part of work done by A in 1 day = 1/12

B can do a piece of work in 15 days

∴ Part of work done by B in 1 day = 1/15

Let,

C can do a piece of work in ‘x’ days

∴ Part of work done by C in 1 day = 1/x

? A, B and C can do the work in 5 days

$(\THEREFORE \frac{1}{{12}} \times 5 + \frac{1}{{15}} \times 5 + \frac{1}{x} \times 5 = 1)$

$(\Rightarrow \frac{5}{{12}} + \frac{1}{3} + \frac{5}{x} = 1)$

⇒ (9/12) + (5/x) = 1

⇒ 5/x = 1 – (9/12)

⇒ 5/x = 3/12

⇒ x = 20

∴ Part of work done by C in 1 day = 1/20

∴ Ratio of part of work done by A, B and C

= 1/12 : 1/15 : 1/20

? LCM of 12, 15 and 20 is 60.

= (1/12) × 60 : (1/15) × 60 : (1/20) × 60

= 5 : 4 : 3

∴ Ratio of money A, B and C get

= 5 : 4 : 3

Given, Total money got by A, B and C together = Rs. 960

∴ Money A gets = {5/(5 + 4 + 3)} × 960 = (5/12) × 960 = Rs. 400