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Example: A can do a job in n days and B can do the same job in m days. How many days it will be required if they work together?
Explore:
In n days A can do 1 portion of job
:. in 1 days A can do 1/n portion of job
In m days B can do 1 portion of job.
:. In 1 days B can do 1/m portion of job
:. If they work together in 1 day they do = (1/n + 1/m) portion = (m +n)/mn portion
(m + n)/mn portion is done in 1 days
:. 1 portion is done is (1 x mn)/(m + n) days
= mn/(m + n)
Answer: mn/(m + n)
Example: A can finish a work in 20 days, which B alone can finish in 30 days. If they build it together and get a payment of $ 500, what is A's share?
Explore:
A's 1 day's work = 1/20 portion
B's 1 day's work = 1/30 portion
Ratio of shares of A & B = 1/20:1/30
= 1/20 x 60: 1/30 x 60
= 3: 2
:. A's share = 500 x 3/5 = $ 300
Answer: $300
Question: 1 If 25 men can unload a truck in 1 hour 30 minutes, how long should it take 15 men to unload the truck?
Option: (a) 2 hours (b) 2 hours 15 minutes (c) 2 hours 20 minutes (d) 2 hours 30 minutes (e) 3 hours
Explore:
1 hours 30 minutes = 90 minutes
25 men can unload the truck in 90 minutes
:. 1 men can unload the truck in (90 x 25) minutes
:. 15 men can unload the truck in (90 x 25)/ 15 minutes
= 150 minutes
= 2 hours 30 minutes
Answer : (d)
Question: 2 If 15 men working in dependently and at the same rate can manufacture 27 baskets in an hour, how many baskets would 45 men working independently and at the same rate manufacture in 40 minutes?
Explore: 40 min = 40/60 hours
15 men in 1 hour manufacture 27 baskets
:. 1 men in 1 hours manufacture 27/15 baskets
:. 45 men in 1 hours manufacture (27 x 45)/ 15 baskets
:. 45 men in 40/60 hour manufacture (27 x 45 x 40)/(15 x 60) baskets
Answer : 54 basket
Question: 3 If a photocopier makes 2 copies in 1/3 second, at the same rate, how many copies does it make in 4 minutes?
Option: (a) 1440 (b) 480 (c) 576 (d) 720 (e) 360
Explore:
Photocopier in 1/3 second makes 2 copies
:. photocopier in 1 second makes (2 x 3)/1 copies
:. photocopier in (4 x 60) second makes (2 x 3 x 4 x 60)
= 1440 copies
Answer : (a)
Question: 4 Four masons can build one sixth of a wall in 3 days. How much of it will be built by six masons in 6 days?
Option: (a) 1/3 (b) 2/3 (c) 1/2 (d) 3/4 (e) 1/6
Explore:
4 masons in 3 days can build 1/6 portion
:. 1 masons in 3 days can build 1/(6 x 4) portion
:. 1 masons in 1 days can build 1/ (6 x 4 x 3) portion
:. 6 masons in 6 days can build (6 x 6)/(6 x 4 x 3) portion
= 1/2 portion
Answer : (c)
Question: 5 A worker makes 4 boxes in 5/3 hours. How many boxes can he make in 50 minutes?
Option: (a) 2 (b) 21/3 (c) 22/3 (d) 25/6 (e) 3
Explore:
5/3 hours = (5/3) x 60 = 100 minutes
:. In 100 minutes the worker makes 4 boxes
:. in 50 minutes the worker makes 4/2 boxes
= 2 boxes
Answer: (a)
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