Rahul, Mohan and Gagan together complete a task. Rahul and Mohan together complete 75 percent of the work and Mohan and Gagan together complete 65 percent of the work. Who is the most efficient of the three?

Question

Rahul, Mohan and Gagan together complete a task. Rahul and Mohan together complete 75 percent of the work and Mohan and Gagan together complete 65 percent of the work. Who is the most efficient of the three?

All are equally efficient.
Mohan
Rahul
Gagan

LohaHridoy

5 views

2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 2 : Mohan

Given:

Rahul, Mohan and Gagan together complete a task.

Rahul and Mohan together complete 75 percent of the work.

Mohan and Gagan together complete 65 percent of the work.

Concept Used:

Time ∝ 1/Efficiency

Calculation:

Let Rahul, Mohan and Gagan take R days, M days and Q days respectively to complete the Work.

Now, According to the question,

(1/R) + (1/M) + (1/G) = 1 ----(i)

(1/R) + (1/M) = (75/100) ----(ii)

and,

(1/M) + (1/G) = (65/100) ----(iii)

Now, Adding equation (ii) and equation (iii),

(1/R) + 2 × (1/M) + (1/G) = (75/100) + (65/100)

⇒ (1/R) + (2/M) + (1/G) = 140/100 ----(iv)

Now, subtracting equation (i) from equation (iv),

⇒ (2/M) - (1/M) = (140 - 100)/100

⇒ 1/M = 40/100

So, from equation (ii),

1/R = (75/100) - (1/M)

⇒ (75/100) - (40/100)

⇒ 1/R = 35/100

Now, from equation (iii),

1/G = (65/100) - (1/M)

⇒ (65/100) - (40/100)

⇒ 1/G = 25/100

Now, Here 1/M > 1/R > 1/G,

This means Mohan's Efficiency > Rahul's Efficiency > Gagan's Efficiency.

∴ Mohan is the most efficient of the three.

For a given amount of work, the number of persons is inversely proportional to the number of working days, i.e. when the number of person increases then working days decrease and vice - versa.

Working efficiency is the work done by an individual in one day and this efficiency is inversely proportional to the number of days to complete a work.

It means that a person who takes fewer days to complete work is said to be more efficient than a person who takes more days to complete the same work.