👷 Men · Days · Hours
1 exam question type, fully solved“If 10 men build a wall in 6 days, how long do 15 men take?” These are men–days problems. They all bend to one master formula — no long thinking, just plug into the chain rule.
The total effort a group puts in is (number of men) × (days) × (hours per day), and that effort is shared across the amount of work . For two situations doing the same kind of work, this stays balanced:
where = men, = days, = hours/day, = amount of work. Drop any quantity that is not mentioned (if hours and work are not stated, set and ).
• How to use it: write everything you know on the left for situation 1, everything for situation 2 on the right, put the unknown as a letter, and cross-multiply.
• Example: 10 men, 6 days. Find days for 15 men. gives days.
Why it works: more men ⇒ fewer days (inverse), more work ⇒ more days (direct). The formula bakes both in, so you never have to decide “multiply or divide” by hand.
12 men finish in 8 days. For 16 men: , so days.
Q140 men complete a work in 18 days. After 6 days, 10 men leave. In how many days is the remaining work completed?
Q220 workers can finish a job in 30 days. 5 more workers join after 10 days. In how many days is the whole job completed?
Q3A work is completed by 35 workers in 30 days. If 5 workers leave after every 10 days, in how many days is the work completed?
Real exam questions — Men · Days · Hours
2 question types · 8 solved examples from real SSC papersTreat a job as a fixed pile of man-days: men times days (times hours/day) stays constant, so when one factor changes the others adjust in inverse proportion.
15 workers complete a work in 20 days. How many workers are needed to complete it in 10 days?
8 men can complete a work in 15 days. In how many days will 12 men complete it?
18 men finish a work in 20 days. In how many days will 24 men finish the same work?
A work can be completed by 35 workers in 30 days. How many workers are needed to finish it in 21 days?