X can complete a work in 12 days, and Y alone can do it in 18 days. They work together for 6 days, and Z completes the remaining work in 3 days. If the total payment for the work is Tk. 600, how much should Z get?

Question: X can complete a work in 12 days, and Y alone can do it in 18 days. They work together for 6 days, and Z completes the remaining work in 3 days. If the total payment for the work is Tk. 600, how much should Z get?

সমাধান:
X-এর একদিনের কাজ = 1/12
Y-এর একদিনের কাজ = 1/18

X ও Y একসাথে ৬ দিন কাজ করে:
= 6 × (1/12 + 1/18)
= 6 × {(3 + 2)/36} = 6 × (5/36) = 30/36 = 5/6

∴ বাকি কাজ = 1 − 5/6 = 1/6

Z এই 1/6 কাজ ৩ দিনে করেছে, অর্থাৎ Z-এর কাজ = 1/6

X-এর কাজ = 6 × 1/12 = 1/2
Y-এর কাজ = 6 × 1/18 = 1/3
Z-এর কাজ = 1/6

তাহলে অনুপাত = 1/2 : 1/3 : 1/6
= 3 : 2 : 1

মোট টাকা = 600
Z-এর অংশ = 1/(3+2+1) = 1/6
∴ Z পাবে = 600 × (1/6) = 100 টাকা