Question

13. Alok takes m times the time taken by Bhola and
Chetan to complete a job. Bhola takes m times the
time taken by Alok and Chetan to complete the
job. Chetan takes m times the time taken by Alok
and Bhola to complete the job. Find m.
2
(a)
(b)
(c)
(d)
(e)
3
4
4
5
5

Answer 1

Answer:

Let the time taken by Bola to complete the job is b days.

Let the time taken by Chetan to complete the job is c days.

So according to first condition -

(1/b) + (1/c) = m/a Equation 1

So according to second condition -

(1/a) + (1/b) = m/c Equation 2

So according to third condition -

(1/a) + (1/c) = m/b Equation 3

Adding (Equation 1, Equation 2 & Equation 3) and solving we get,

Answer is m = 2

Step-by-step explanation:

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Answer 2

The answer is (a) 2.

Let's assume that Alok takes x amount of time to complete the job

Then we have:

Bhola takes $m*x$ amount of time to complete the job.

Chetan takes $m^2*x$ amount of time to complete the job (since Chetan takes m times the time taken by Alok to complete the job, and Alok takes x time).

Bhola takes $mm^2x = m^3*x$ amount of time to complete the job (since Bhola takes m times the time taken by Chetan to complete the job).

Since they all complete the same job, we have:

$1/x + 1/(mx) + 1/(m^2x) = 1$

Multiplying both sides by$1/x + 1/(mx) + 1/(m^2x) = 1$we get:

$m^2 + m + 1 = m^3$

Rearranging, we get:

$m^3 - m^2 - m - 1 = 0$

This is a cubic equation that can be solved using various methods.

One possible method is to use the rational root theorem to find a rational root (if one exists), and then factor the equation using polynomial long division. However, this can be quite time-consuming.

Alternatively, we can notice that m=2 is a solution to the equation.

We can verify this by plugging m=2 into the equation and checking that it satisfies the equation:

$2^3 - 2^2 - 2 - 1 = 8 - 4 - 2 - 1 = 1 - 1 - 1 - 1 = 0$

Therefore, the answer is (a) 2.

For similar question on polynomial equation

https://brainly.in/question/33850300

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