Question

(i)If 64 men can do a job in 20 days, how many men will be needed to complete the work in 16 days.
(ii) The age of Sam & Ram are in the ratio 3:5. After 7 years, the sum of their ages will be 94. What are their
present ages?

Answer 1

Answer:

i) 80 workers

ii) Sam is 30 years old and ram is 50 years old at present

Answer 2

(i) 80 men will be needed to complete the work in 16 days.

(ii) The present ages of Sam and Ram are 30 years and 50 years respectively.

(i) Given,

Number of men = 64

Number of days in which 64 men complete a work = 20

Number of days in which 16 men can complete the same work = ?

• Since 64 men take 20 days to complete a work, more number of men would be required to complete the same work in 1 day (inverse proportion).

∴  Number of men required to complete the work in 1 day = 64 × 20

• Now, number of men required to complete the work in 16 days will be lesser than that required to complete the work in 1 day.

=> Number of men required to complete the work in 16 days = (64 × 20) / 16 = 4 × 20 = 80

• Therefore, 80 men will be required to complete the work in 16 days.

(ii)  Given,

Ratio of the ages of Sam and Ram = 3 : 5

=> Present age of Sam = 3x years

Present age of Ram = 5x years

• Age of Sam after 7 years will be (3x + 7) years.

Age of Ram after 7 years will be (5x + 7) years.

• According to the question,

(3x + 7) + (5x + 7) = 94

Or, 3x + 7 + 5x + 7 = 94

Or, 8x + 14 = 94

Or, 8x = 94 - 14

Or, 8x = 80

Or, x = 80 / 8

Or, x = 10

• Therefore, the present of Sam = 3x years = (3 × 10) years = 30 years

Present age of Ram = 5x years = (5 × 10) years = 50 years