# Pooja and Ritu can do a piece of work in $17\dfrac{1}{7}$ days. If one day work of Pooja be three fourth of one day work of Ritu; find in how many days each will do the work alone?

(a) Pooja in 44 days and Ritu in 8 days

(b) Pooja in 80 days and Ritu in 500 days

(c) Pooja in 20 days and Ritu in 120 days

(d) Pooja in 40 days and Ritu in 30 days

Answer

Verified

362.7k+ views

Hint: We solve this problem by using the fact by assuming that amount of work done by Pooja be $\dfrac{1}{a}$and the work done by Ritu be $\dfrac{1}{b}$(where a and b are the number of days required for Pooja and Ritu to do the work respectively). The trick is to assume work done to be inversely related to the number of days and then proceed with the problem to satisfy the necessary conditions.

Complete step-by-step answer:

We have,

$\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{7}{120}$ -- (1)

To explain why work done should be inversely related to the number of days to complete the work, let us assume two cases. In the first case, Pooja takes 2 days to complete a work and in the second case, Pooja takes 5 days to complete a work. Clearly, the amount of work done in the first case is more since she was able to finish the same amount of work in less number of days. Thus, the amount of work done should be inversely related to the number of days to complete the task.

Thus, in this case, amount of work done is inversely proportional to $17\dfrac{1}{7}$, this is-

=$\dfrac{1}{17\dfrac{1}{7}}$

=$\dfrac{7}{120}$(as we have in (1))

Also, from second condition, we have,

$\dfrac{1}{a}=\dfrac{3}{4}\times \dfrac{1}{b}$ -- (2)

Putting value of (2) in (1), we get,

$\dfrac{3}{4b}+\dfrac{1}{b}=\dfrac{7}{120}$

$\dfrac{7}{4b}=\dfrac{7}{120}$

b=30

Also, from (2), we have,

$\dfrac{1}{a}=\dfrac{3}{4}\times \dfrac{1}{b}$

a=$\dfrac{4b}{3}$

a=$\dfrac{4\times 30}{3}$

a=40

Hence, Pooja takes 40 days and Ritu takes 30 days to complete the work alone respectively.

Hence, the correct answer is (d).

Note: While solving problems related to the calculating work done by a single person when work done by both people is given, we have to understand that the number of days required for 1 person to complete the work is more than the number of days required for both combined to complete the same work. Once we keep this in mind, we can easily solve the problem by using the inverse relation between work done and number of days required to complete the work.

Complete step-by-step answer:

We have,

$\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{7}{120}$ -- (1)

To explain why work done should be inversely related to the number of days to complete the work, let us assume two cases. In the first case, Pooja takes 2 days to complete a work and in the second case, Pooja takes 5 days to complete a work. Clearly, the amount of work done in the first case is more since she was able to finish the same amount of work in less number of days. Thus, the amount of work done should be inversely related to the number of days to complete the task.

Thus, in this case, amount of work done is inversely proportional to $17\dfrac{1}{7}$, this is-

=$\dfrac{1}{17\dfrac{1}{7}}$

=$\dfrac{7}{120}$(as we have in (1))

Also, from second condition, we have,

$\dfrac{1}{a}=\dfrac{3}{4}\times \dfrac{1}{b}$ -- (2)

Putting value of (2) in (1), we get,

$\dfrac{3}{4b}+\dfrac{1}{b}=\dfrac{7}{120}$

$\dfrac{7}{4b}=\dfrac{7}{120}$

b=30

Also, from (2), we have,

$\dfrac{1}{a}=\dfrac{3}{4}\times \dfrac{1}{b}$

a=$\dfrac{4b}{3}$

a=$\dfrac{4\times 30}{3}$

a=40

Hence, Pooja takes 40 days and Ritu takes 30 days to complete the work alone respectively.

Hence, the correct answer is (d).

Note: While solving problems related to the calculating work done by a single person when work done by both people is given, we have to understand that the number of days required for 1 person to complete the work is more than the number of days required for both combined to complete the same work. Once we keep this in mind, we can easily solve the problem by using the inverse relation between work done and number of days required to complete the work.

Last updated date: 28th Sep 2023

â€¢

Total views: 362.7k

â€¢

Views today: 8.62k

Recently Updated Pages

What do you mean by public facilities

Difference between hardware and software

Disadvantages of Advertising

10 Advantages and Disadvantages of Plastic

What do you mean by Endemic Species

What is the Botanical Name of Dog , Cat , Turmeric , Mushroom , Palm

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

One cusec is equal to how many liters class 8 maths CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

How many millions make a billion class 6 maths CBSE

How many crores make 10 million class 7 maths CBSE

What is meant by shramdaan AVoluntary contribution class 11 social science CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE