Question

A can dig a trench in \[6\] days while B can dig it in \[8\] days. They dug the trench working together and received RS. \[1120\] for it. Find the share of each in it

Answer 1

Hint: In this problem, the word problem is solved by converting the data in a mathematical way then, we need to calculate the share of each work when they are digging together then the received amount is RS. \[1120\] . Time and work problems deal with the simultaneous performance involving the efficiency of an individual or a group and the time taken by them to complete a piece of work. The number of workers is inversely proportional to the time taken to complete the work, \[\dfrac{1}{T}\] . Where, \[T - \] certain amount of time.

Complete step by step solution:
In this given problem,
A can dig a trench in \[6\] days.
B can dig a trench in $ 8 $ days
Received amount is RS. \[1120\]
To find the share of each work, we get
According to the time and work method, The number of workers is inversely proportional to the time taken to complete the work, \[\dfrac{1}{T}\] .
Where, \[T - \] certain amount of time.
In \[6\] days A can dig \[ = 1\] trench
In \[1\] day A can dig \[ = \dfrac{1}{6}\] trench
In \[8\] days B can dig \[ = 1\] trench
In \[1\] day B can dig \[ = \dfrac{1}{8}\] trench
The ratio of the efficiencies of two workers is inversely proportional to the time taken by them to complete a work, we get
So, The ratio of A and B work is \[\dfrac{1}{6}:\dfrac{1}{8}\]
Therefore, the ratio is \[4:3\]
Total \[ = 4 + 3 = 7\]
To calculate the share of A and B, we get
Share of A is \[\dfrac{4}{7} \times 1120 = 4 \times 160 = 640\]
Share of B is Total share value \[ - \] A’s share \[ = 1120 - 640 = 480\]
Finally, we got the share value of A is Rs.\[640\] and B is Rs.\[480\].

Note: We need to solve the word problem converted into mathematical form, on comparing the work and time formula with the question to get the share of each work. The ratio of the efficiencies of two workers is inversely proportional to the time taken by them to complete a work. If a worker is less efficient than he/she will take more time to complete the work. The number of workers is inversely proportional to the time taken to complete the work.