Try to solve the following time and work questions using time and work formula:
Q.1.Ram is twice as efficient as Sunita and can finish a piece of work in 25 days less than Sunita. Sunita can finish this work in how many days?
a) 45 Days
b) 30 Days
c) 90 Days
d) 25 Days
e) 50 Days
Sol : Option E Explanation:Work Formula: Efficiency of Ramesh: Efficiency of Sunita = 2: 1.
Ram will take 1/2 of time as compared to Sunita.
Say, Sunita takes 2x days and Ram takes x days. ∴ 2x – x = 25 ⇒ x = 25.
∴Sunita takes 25 × 2 = 50 days to do the work.
Q.2. A can do a piece of work in 16 days, and B can do the same work in 12 days. With the help of C, they finished the work in 6 days. C can do the work in how many days, working alone?
a) 48 Days
b) 24 Days
c) 30 Days
d) 32 Days
e) 40 Days
Sol : Option A Explanation:C alone will take 1/6 – 1/12 – 1/16 = 1/48 = 48 days to complete the work
Q.3. Chetan is thrice as efficient as Mamta and together they can finish a piece of work in 60 days. Mamta will take how many days to finish this work alone?
a) 80 Days
b) 160 Days
c) 240 Days
d) 320 Days
e) 400 Days
Sol : Option C Explanation:Chetan is thrice as efficient as Mamta. Let, Mamta takes 3x days and Chetan takes x days to complete the work. ∴ 1/x + 1/3x = 1/60 ⇒ x = 80. ∴ Mamta will take 80 × 3 = 240 days to complete the work.
Q.4.Mr. Ram has a sum of money, which is sufficient to pay Usha's wages for 30 days and Manika's wages for 60 days. If he employs them together, the money is sufficient to pay their wages for how many days?
a) 12 Days
b) 10 Days
c) 30 Days
d) 20 Days
e) 36 Days
Sol : Option D Explanation:The concept is the same here as the normal time and work problems. Usha’s one day’s wage bill is 1/30 of the total money. Manika’s wage bill is 1/60 of the total money. That means together their wage bill is 1/30 + 1/60 = 3/60 = 1/20 of the total money. Thus, the money is sufficient for their 20 days’ wages.
Q.5.X can do a piece of work in 20 days. He worked at it for 5 days and then Y finished it in 15 days. In how many days can X and Y together finish the work?
a) 10 Days
b) 15 Days
c) 18 Days
d) 24 Days
e) 32 Days
Sol : Option A Explanation: X’s five day work = 5/20 = 1/4. Remaining work = 1 – 1/4 = 3/4.
This work was done by Y in 15 days. Y does 3/4th of the work in 15 days, he will finish the work in 15 × 4/3 = 20 days. \ X & Y together would take 1/20 + 1/20 = 2/20 = 1/10 i.e. 10 days to complete the work.
Q.6.X can do a piece of work in 30 days. Y can do it in 20 days, and Z can do it in 24 days. In how many days will they all do it together?
a) 6 Days
b) 5 Days
c) 4 Days
d) 4 2/3 Days
e) 8 Days
Sol : Option E Explanation:They all will take 1/30 + 1/20 + 1/24 = 1/8. ⇒ 8 days to complete the work
Q7.M and N can do a piece of work in 8 days and O can do it in 24 days. In how many days will M, N, and O do it together?
a) 6 Days
b) 5 Days
c) 4 Days
d) 4 2/3 Days
e) 3 Days
Sol : Option A Explanation:They will together take 1/8 + 1/24 = 1/6 ⇒ 6 days to finish the work.
Q8.One man can paint a house in, '10' days and another man can do it in 15 days. If they work together, they can do it in 'd' days, then the value of 'd' is
a) 6 Days
b) 8 Days
c) 12 Days
d) 10 Days
e) 3 Days
Sol : Option A Explanation:Total time is d when they are working together = 1/10 + 1/15 = 1/6. ⇒ 6 days to complete the work.
Q9.A can do a piece of work in 9 days and B in 18 days. They begin together, but A goes away three days before the work is finished. The work lasts for
a) 6 Days
b) 8 Days
c) 12 Days
d) 10 Days
e) 3 Days
Sol : Option B
Let the work lasts for x days.
B works for x days and A works for x – 3 days. ∴ (x-3)/9 + (x/18) = 1 ⇒ x = 8
Q10.It takes 'h' hours to mow a lawn. In one hour what part of the lawn is mowed?
a) h - 1
b) 1 - h
c) 1 / h
d) h / (1 + h)
e) h
Sol : Option C Explanation:Total time to mow a lawn = h. ∴ In one hour lawn mowed = 1/h.