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Algebra Level 2

Work done by ( x − 3 ) (x-3) men in ( 2 x + 1 ) (2x+1) days and the work done by ( 2 x + 1 ) (2x+1) men in ( x + 4 ) (x+4) days are in the ratio 3 : 10 3:10 .

Find the value of x x .

NOTE: Please give a suitable explaination if you have time. Thank you


The answer is 6.

Rishabh Tripathi by Rishabh Tripathi , 22, India

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4 solutions

Vasudev Chandna
Mar 25, 2015

Since they are in direct proportion, multiply Men(1)/Days(1) and Men(2)/Days(2) where 1 and 2 are cases given in question.

You'll get this equation-

=> (x-3)/(2x+1)*(2x+1)/(x+4) = 3/10

=> 10(x-3) = 3(x+4)

=> 10x-30 = 3x+4

=> 7x = 42

=> x=6

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Ankit Kumar Jain
Mar 16, 2015

The equation would be ( x − 3 ) × ( 2 x + 1 ) ( 2 x + 1 ) × ( x + 4 ) = 3 10 \frac{{(x-3)}\times{(2x+1)}}{{(2x+1)}\times{(x+4)}} = \frac{3}{10} .. Solve it and you get the answer 6.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Venture Hi
Mar 7, 2015

Convert work done into man-days. So, for 1 man in 1 day can complete 1/(x-3)* 1/(2x+1) * (3/13) th of a certain project. Also, amount work done by 1 man in 1 day is 1/(2x+1) 1/(x+4) (10/13) th of the same project.Hence, we can conclude that both equation are equal and therefore, solve for x.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Steven Nguyen
Oct 5, 2015

Ignore the amount of days since they are equal.

(X-3)/(x+4) = 3/10

× = 6

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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