P takes twice as much time as Q or three times as much time as R to finish a piece of work. Working together, they can finish the work in 2 days. Q can do the work alone in how many days?

Question: P takes twice as much time as Q or three times as much time as R to finish a piece of work. Working together, they can finish the work in 2 days. Q can do the work alone in how many days?

Solution:
ধরা যাক,
P, Q ও R এর যথাক্রমে কাজটি শেষ করতে সময় লাগে x, x/2, এবং x/3 দিন।

তারা একসাথে 2 দিনে কাজ শেষ করে।
অর্থাৎ তাদের একদিনের কাজ হলো 1/2 অংশ।

∴ P + Q + R এর একদিনের কাজ = (1/x) + (2/x) + (3/x)
= (1 + 2 + 3)/x
= 6/x

শর্তমতে,
6/x = 1/2
∴ x = 12

∴ Q একা কাজ শেষ করতে সময় নেবে = 12/2 = 6 দিন।