A and B can complete a certain task together in 30 days. After A works for 16 days, B is left to finish the remaining work by himself in 44 days. How many days would it take for B to complete the entire task on his own?

Correct — C.
Let A do a and B do b of the task per day. Together: a + b = 1⁄30.
Whole task: 16a + 44b = 1
Split B's 44 days as 16 + 28: 16(a + b) + 28b = 1

16 × 1⁄30 + 28b = 1, so 28b = 1 − 8⁄15 = 7⁄15
b = 7⁄15 ÷ 28 = 1⁄60 of the task per day
B alone takes 60 days → option (c)

Why the others are wrong

• (a)
  40 days — 40 days makes B's rate 1⁄40 and A's 1⁄30 − 1⁄40 = 1⁄120. Then 16⁄120 + 44⁄40 = 37⁄30, more than the whole task.
• (b)
  50 days — 50 days makes A's rate 1⁄30 − 1⁄50 = 1⁄75. A's 16 days and B's 44 would then finish 16⁄75 + 44⁄50 = 82⁄75, more than one task.
• (d)
  70 days — 70 days makes A's rate 1⁄30 − 1⁄70 = 2⁄105. Then 16 × 2⁄105 + 44⁄70 = 14⁄15, short of the whole task.

When a pair's combined time is known, regroup the individual days into days of the pair. A's 16 days plus B's first 16 days are 16 days of A and B together, which finish 16⁄30 of the task.

B's remaining 28 days do the rest, 14⁄30, so B alone does 1⁄60 a day.

Key facts

• If A and B together take 30 days, a + b = 1⁄30 of the task per day.
• 16 days of A plus 16 days of B equal 16 days of A and B working together.
• Here both rates are 1⁄60 a day: 16⁄60 + 44⁄60 = 1.

Common traps

• Reading 'after A works for 16 days' as A and B together for 16 days, which leads to about 94.3 days.
• Adding 16 + 44 = 60 as a rule. It works here only because A and B turn out equally fast.

No directly related past PYQ was found.