Unitary Method
ICSE · Class 7 · Mathematics
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Quick Quiz: Unitary Method
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A and B together complete a piece of work in 2 2/5 days. A alone completes the work in 4 days. How long does B alone take to complete the same work?
A tap fills 1/4 of a cistern in 1 hour and another tap empties 1/6 of the cistern in 1 hour. If both taps are open together, how long will the cistern take to fill when it starts empty?
A watch gains 42 seconds in 80 hours. How many hours will it take to gain 2 minutes 6 seconds?
135 kg of corn feeds 45 horses for 8 days. For how many days will the same quantity of corn feed 24 horses?
Sample Questions
Ajay and Vijay together paint a hall in 6 days. Ajay alone paints it in 8 days. In how many days can Vijay alone paint the hall?
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24 days
Ajay and Vijay together paint 1/6 of the hall in 1 day. Ajay paints 1/8 of the hall in 1 day. Vijay's 1 day's work = 1/6 - 1/8 = 4/24 - 3/24 = 1/24. So Vijay alone takes 24 days.
A and B can do a piece of work in 15 days and 20 days respectively. How much work will be left after A works alone for 3 days?
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4/5 of the work
A's 1 day's work = 1/15. In 3 days, A completes 3 x 1/15 = 1/5 of the work. Work left = 1 - 1/5 = 4/5. So 4/5 of the work is left.
A man earns ₹400 in 10 days. Using the unitary method, how much will he earn in 28 days?
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₹1,120
In 10 days, earnings = ₹400. In 1 day, earnings = ₹400/10 = ₹40. In 28 days, earnings = 28 x ₹40 = ₹1,120. So the answer is ₹1,120.
0.75 m of cloth costs ₹45. What is the cost of 0.6 m of the same cloth?
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₹36
0.75 m costs ₹45, so 1 m costs ₹45/0.75 = ₹60. Then 0.6 m costs 0.6 x ₹60 = ₹36. So the answer is ₹36.
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