1200 Men Can Construct A Wall Of Length 1500 Metres In 30 Days. In How Many Days Can Half The Previous Strength Construct 1800 Metres Of Wall Working 1/3Rd More Time Per Day Than In The Previous Case?
Answers
Given : 1200 Men Can Construct A Wall Of Length 1500 Metres in 30 Days.
To Find : In How Many Days Can Half The Previous Strength Construct 1800 Metres Of Wall Working 1/3rd More Time Per Day Than in The Previous Case
Solution:
1200 Men Can Construct A Wall Of Length 1500 Metres in 30 Days.
=> 1200 * 30 = 36000 Man day = 1500 m
=> 1 man day = 1500/36000 m
=> 1 Man day = 15/360 m
=> 1 Man day = 1/24 m
Half The Previous Strength = (1/2) * 1200 = 600 Men
Working 1/3rd More Time Per Day = 1 + 1/3 = 4/3 Day
Let work is finished in D days
Total Man days = 600 * ( 4/3 ) * D
= 800D man Days
1 Man day = 1/24 m
=> 800D man days = 800 D * 1/24 m
800 D * 1/24 = 1800 m
=> D = 1800 * 24 / 800
=> D = 18 * 3
=> D = 54
54 Days
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54 days
Step-by-step explanation:
Let x be the no. of hours of work done daily and y be the number of days for completing the wall.
In Ist case,
Work Done = 1500 (∵given)
No. of men = 1200
No. of days = 30
so,
Work done in one day ⇒ (1200 * 30 * x)/1500
⇒ 36000x/1500
= 24 x
A.T.Q.
In IInd case,
Strength = 1200/2 = 600
Work Done = 1800
Work done per day = x + x/3
so,
⇒ [(600x (x + x/3)xy]/1800 = 24x
= 800xy/1800 = 24x
= 8xy/18 = 24x
= 4xy/18 = 54x
∵ y = 54
Thus, 54 days would be required to complete the work.
Learn more: Find the number of days required to complete the work
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