Unitary Method
- Nine examiners can examine a certain number of answer books in 12 days by working 5 hours a day. How many hours in a day should 4 examiners work to examine twice the number of answer books in 30 days?
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Here , M1 = 9
D1 = 12
H1 = 5
W1 = 1
And M2 = 4
D2 = 30
H2 = x
W2 = 2
We know that ,∴ M1 x D1 x H1 = M2 x D2 x H2 W1 W2 ⇒ 9 x 12 x 5 = 4 x 30 x H2 1 2
Correct Option: A
Here , M1 = 9
D1 = 12
H1 = 5
W1 = 1
And M2 = 4
D2 = 30
H2 = x
W2 = 2
We know that ,∴ M1 x D1 x H1 = M2 x D2 x H2 W1 W2 ⇒ 9 x 12 x 5 = 4 x 30 x H2 1 2
⇒ H2 = 9 hours
Hence required answer = 9 hours .
- A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:
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As per the given question ,
Food of 150 men for 45 days = 150 × 45 = 6750 unit
After 10 days , Food of 150 men for 150 × 10 = 1500 unit
And after 10 days remaining men = 150 - 25 = 125
and remaining food = 6750 - 1500 = 5250 unit
Let D be the number of days for which the remaining food .Correct Option: C
As per the given question ,
Food of 150 men for 45 days = 150 × 45 = 6750 unit
After 10 days , Food of 150 men for 150 × 10 = 1500 unit
And after 10 days remaining men = 150 - 25 = 125
and remaining food = 6750 - 1500 = 5250 unit
Let D be the number of days for which the remaining food .
So, 125 × D = 5250
⇒ D = 5250 /125 = 42 days
- Nine engines consume 24 metric tonnes of coal, when each is working 8 hours day. How much coal is required for 8 engines, each running 13 hours a day, if 3 engines of former type consume as much as 4 engines of latter type?
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Let required amount of coal be y metric tonnes .
9 engines consumes 24 metric tonnes of coal in 8 hours a day.
More engines, more amount of coal (direct proportion)
If 3 engines of first type consume 1 unit, then 1 engine will consume 1/3 unit which is its the rate of consumption.
If 4 engines of second type consume 1 unit, then 1 engine will consume 1/4 unit which is its the rate of consumption
More rate of consumption, more amount of coal (direct proportion)
More hours, more amount of coal(direct proportion)Correct Option: D
Let required amount of coal be y metric tonnes
9 engines consumes 24 metric tonnes of coal in 8 hours a day.
More engines, more amount of coal (direct proportion)
If 3 engines of first type consume 1 unit, then 1 engine will consume 1/3 unit which is its the rate of consumption.
If 4 engines of second type consume 1 unit, then 1 engine will consume 1/4 unit which is its the rate of consumption
More rate of consumption, more amount of coal (direct proportion)
More hours, more amount of coal(direct proportion)
Now we have , 9 × ( 1 / 3 ) × 8 × y = 8 × ( 1 / 4 ) × 13 × 24
⇒ 3 × 8 × y = 8 × 6 × 13
⇒ 3 × y = 6 × 13 ⇒ y = 2 x 13 = 26 metric tonnes
- Some persons can do a piece of work in 12 days. Two times the number of such persons will do half of that work in :
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Let M men can do the in 12 days and the required number of days be D.
More men, Less days [ Indirect Proportion ]
Less work, Less days [ Direct Proportion ]
By chain rule ,⇒ 2M x 1 x D = M x 1 x 12 2 Correct Option: D
Let M men can do the in 12 days and the required number of days be D.
More men, Less days [ Indirect Proportion ]
Less work, Less days [ Direct Proportion ]
By chain rule ,⇒ 2M x 1 x D = M x 1 x 12 2
⇒ D = 3 days
Thus , required answer is 3 days .
- 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?
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As per the given question,
M1 = 36 Men , D1 = 18 days , W1 = 1
M2 = 27 Men , D2 = ? , W2 = 1
We know that ,⇒ M1D1 = M2D2 W1 W2 Correct Option: A
As per the given question,
M1 = 36 Men , D1 = 18 days , W1 = 1
M2 = 27 Men , D2 = ? , W2 = 1
We know that ,⇒ M1D1 = M2D2 W1 W2 ⇒ 36 x 18 = 27 x D2 1 1
⇒ D2 = 4 x 6 = 24 days
Therefore , 27 men will complete the same work in 24 days .
