Answer

Correct Answer : b ) 7

Trick Method:

As we can see 

(3n - 1) * (2n + 1) mendays = x work units.

(3n + 1) * (4n - 3) mendays = y work units.

x : y = 6 : 11

we can try checking x and y ratio for values of n given in the options:

For n = 6, x = 204, y = 399

x / y = 204 / 399 = 68 / 133, which is not equal to 6 / 11.

For n = 7, x = 300, y = 550

x / y = 300 / 550 = 6 / 11, which is equal to 6 / 11.

Hence, (b) is the correct answer.

Basic Method:

As per the question,

(3n - 1) men take (2n + 1) days to complete x work units.

(3n + 1) men take (4n - 3) days to complete y work units.

x : y = 6 : 11 ........(1)

It can be said that,

(3n - 1) * (2n + 1) mandays = x unit of work .......(2)

(3n + 1) * (4n - 3) mandays = y unit of work .......(3)

From (2) and (3),

[(3n - 1) * (2n + 1)] / [(3n + 1) * (4n - 3)] = x / y ........(4)

From (1), x / y = 6 / 11 ...........(5)

Equating (4) and (5)

[(3n - 1) * (2n + 1)] / [(3n + 1) * (4n - 3)] = 6 / 11

(6n² + 3n - 2n - 1) / (12n² - 9n + 4n - 3) = 6 / 11

11 * (6n² + 3n - 2n - 1) = 6 * (12n² - 9n + 4n - 3)

66n² + 33n - 22n - 11 = 72n² - 54n + 24n - 18

6n² - 41n - 7 = 0

6n² - 42n + n - 7 = 0

6n(n - 7) + 1(n - 7) = 0

(6n + 1) * (n - 7) = 0

n = -1/6, n = 7

If n is -1/6, then (3n - 1) men will be -3 men, the number of men cannot be negative.

So, n = 7 as it also satisfies the conditions.

Hence, (b) is the correct answer.

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