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Where Every Arithmetic Section Starts
Time & Work is the most reliably scored chapter in the whole arithmetic section — and the one candidates most often waste their clock on. The reason is simple: most people solve it with fractions. One-twelfth plus one-eighteenth, find the LCM of the denominators, invert the answer. Three minutes gone, and one arithmetic slip away from a wrong option.
There is a faster way. Stop treating the job as *1 unit* of work and start treating it as a *number of units* — specifically the LCM of the given days. Suddenly every rate is a whole number, every addition is mental, and a two-minute question becomes a fifteen-second one.
The same idea covers pipes and cisterns, wages and man-days problems, because all four are the same question wearing different clothes: something is being done at a steady rate, and you are asked how long it takes.
1. A can finish a piece of work in 12 days and B in 18 days. Working together, how long will they take?
2. A is twice as efficient as B. Working together they complete a job in 12 days. How long would A alone take?
3. A pipe can fill a tank in 6 hours, but because of a leak in the bottom it takes 8 hours. How long will the leak alone take to empty a full tank?
4. If 12 men can complete a piece of work in 18 days, how many days will 27 men take to complete the same work?
5. A alone can do a work in 20 days and B alone in 30 days. They work together for 4 days, after which A leaves. In how many more days will B finish the remaining work?
6. Two pipes can fill a tank in 20 minutes and 30 minutes respectively. If both are opened together, how long will the tank take to fill?
7. 6 men or 9 women can complete a piece of work in 12 days. How long will 4 men and 3 women take to complete the same work?
8. A can do a work in 6 days and B in 8 days. With C's help they finish it in 3 days and are paid ₹1200 in total. What is C's share of the wages?