The work done by (x+3) labourers in (x-2) days and the work done by (x-2) labourers in (x+5) days are in the ratio 4:5. Value of x is....
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Answer:
Step-by-step explanation:
Work done by (x-3) men in (2x+1) days and (2x+1) men in (x+4) days is in ratio 3:10. What is the value of x? How do I approach to a solution?
When x-3 people complete the work in 2x+1 days this means work done in one day is equal to 2x+1/x-3.
And when 2x+1 workers complete the work in x+4 days this means work done in ome day is equal to x+4/2x+1.
As the total work is in the ratio of 3:10 the worl done in one day also will be in the ratio of 3:10
So 2x+1/x-3/x+4/2x+1 = 3/10
(2x+1)^2/(x-3)(x-4) = 3/10
4x^2 + 1 + 4x/x^2 + 12 - 7x = 3/10
Cross multiplying we get
10 (4x^2 + 1 + 4x) = 3(x^2 + 12 - 7x)
40x^2 + 10 + 40x = 3x^2 + 36 - 21x
Taking all terms in RHS to the left we get
37x^2 + 61x - 26 =0
Splitting the middle term we get
37x^2 + 74x - 13x -26 =0
37x(x+2) -13(x+2) =0
(37x - 13)(x+2) =0
x = 13/37 or -2
Check by putting values of x in the original equation. If the ratio come out to be 3:10 then the answer is correct.