Shortcut:
X, Y and Z can do a work in a, b and c days respectively. If they work together they get an amount of Rs M, then the share of
X = Rs
Mbc
/
ab + ac + bc
Share of Y = Rs
Mac
/
ab + ac + bc
Share of Z = Rs
Mab
/
ab + ac + bc
and ratio of their shares is X : Y : Z = bc : ac : ab
Here, a = 6, b = 10, c = 12, M = 4200
Using these values in shortcut, we get:
Share of C = Rs
4200 x 6 x 10
/
6 x 10 + 6 x 12 + 10 x 12
= Rs
4200 x 6 x 10
/
60 + 72 + 120
= Rs
4200 x 6 x 10
/
252
= Rs
4200 x 10
/
42
= 100 x 10 = 1000
Hence, the share of C is Rs 1000.
