40 men can finish 45 kg of rice in 25 days . 20 men can finish 45 kg of rice in __ days
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Class 11
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>>Numerical Applications
>>Time and work
>>If 40 persons consume 240 kg of rice in
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If 40 persons consume 240 kg of rice in 15 days, in how many days will 30 persons consume 48 kg of rice?
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Correct option is C)
We first find out in which variations are the quantities related in the given situation.
When the number of people decreases from 40 to 30, the number of days to consume the rice will be more.
When the number of kg of rice decrease from 240 kg to 48 kg, number of days to consume will be less.
Hence, the number of days is in direct variation with the number of kg of rice and in inverse variation with the number of people.
Since number of days and number of kg of rice are in direct variation,
Constant of variation k
1
=
240
48
Since number of days and number of people are in inverse variation,
Constant of variation k
2
=
30
40
Now x=k
1
×k
2
×15
=
30
40
×
240
48
×15
=4
Hence, 30 people will consume 4 kg of rice in 4 days.
20 men can finish 45 kg of rice in 50 days if 40 men can finish 45 kg of rice in 25 days
Given:
- 40 men can finish 45 kg of rice in 25 days .
To Find:
- 20 men can finish 45 kg of rice in how many days?
Solution:
Step 1:
40 men can finish 45 kg of rice in 25 days
=> Rice needed for 40 x 25 = 1000 Man days is 45 kg
Step 2:
Assume 20 men can finish 45 kg of rice in d days
=> Rice needed for 20 x d Man days is 45 kg
Step 3:
As Rice Quantity is same hence equate man days and solve for d
20 x d = 1000
=> d = 50 ( Divide both sides by 20)
Hence, 20 men can finish 45 kg of rice in 50 days