Question

40 men could have finished the whole project in 28 days but due to the inclusion of a few more men, work got done in ¾ of the time. find the ratio of number of new men to number of old men.

Answer 1

Find the number days needed to complete the work when more men were needed:

Number of days = 3/4 x 28 = 21 days

40 men took 28 days (Given)

⇒28 days = 40 men

Find number of men needed for the job to be completed in 1 day:

28 days = 40 men

1 day = 40 x 28 = 1120 men

Find number of men needed for the job to be completed in 21 day:

1 day = 1120 men

21 days = 1120 ÷ 21 = 160/3 = 53 1/3 men

Find the addition of men:

53 1/3 - 40 = 13 1/3 = 40/3

Find the ratio of old men : new men

old men : new men = 40 : 40/3

Multiply by 3:

old men : new men = 120 : 40

Divide by 40:

old men : new men = 3 : 1

Answer: The ratio is 3 : 1