Ram and Shyam can complete a work in 12 and 18 days respectively. They worked together and received ₹15,000 for doing the work. How much money did they receive individually?

Correct option is B

Given:

Ram can complete the work in 12 days.

Shyam can complete the work in 18 days.

Total payment for the work = ₹15,000

Formula Used:

​$$\text{Efficiency} = \frac{1}{\text{Time taken to complete the work}}$$​​​

Ratio of shares = Ratio of efficiencies

Solution:

Calculate individual efficiencies:

Ram's efficiency = $$\frac{1}{12}$$​​

Shyam's efficiency = $$\frac{1}{18}$$​​

Calculate the ratio of their efficiencies:

Ratio of Ram's efficiency to Shyam's efficiency = $$\frac{1}{12}$$​ : $$\frac{1}{18}$$​ = 3 : 2

Divide the total payment based on their efficiency ratio:

Ram's share = $$\frac{3}{(3+2)} \times$$​ ₹15,000 =  $$\frac{3}{5} \times$$​₹15,000 = ₹9,000

Shyam's share =  $$\frac{2}{(3+2)} \times$$​₹15,000 = $$\frac{2}{5} \times$$​ ₹15,000 = ₹6,000

Therefore, Ram received ₹9,000 and Shyam received ₹6,000.

Option (b) is right answer.

Alternate Method:

​Formula Used:

T _(A+B+C)=$$\frac{\text {Total Work}}{ E_A + E_B+ E_C}$$

Solution:

Ratio of Ram's efficiency to Shyam's efficiency =3 : 2

Ram's share= $$\frac{3}{5} \times$$​​₹15,000 = ₹9,000

Shyam's share=  $$\frac{2}{5} \times$$​​₹15,000 = ₹6,000

Option (b) is right answer.

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