Question

The work done by (x-3) men in (2x+1) days to the work done by (2x+1) men in (x+4) days is in the ratio of 3:10. Find x.

Answer 1

atq (x-3)(2x+1)/(2x+1)(x+4)=3:10
x(2x+1)-3(2x+1)/2x(x+4)+1(x+4)=3:10
(2x2+x-6x-3)/(2x2+8x+x+4)=3:10
(2x2-5x-3)/(2x2+9x+4)=3:10
3(2x2+9x+4)=10(2x2-5x-3)
6x2+27x+12=20x2-50x-30
14x2-77x-42=0
2x2-11x-6=0
2x2-12x+x-6=0
2x(x-6)+1(x-6)=0
(2x+1)(x-6)=0
x=6
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Answer 2

Answer:

Step-by-step explanation:

Given :-

Work done by (x - 3) men in (2x + 1) days

And the work done by (2x+1) men in (x + 4) days

Ratio of days = 3 : 10

To Find :-

The Value of x.

Solution :-

I men does work in (x - 3)(2x + 1) days

I men does the work in (2x+1)(x + 4) days

According to the Question,

Ratio of works = 3 : 10

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

⇒ (x - 3)/(x + 4) = 3/10

⇒ 10(x - 3) = 3(x + 4)

⇒ 10x - 30 = 3x + 12

⇒ 10x - 3x = 12 + 30

⇒ 7x = 42

⇒ x = 42/7

⇒ x = 6

Hence the required value of x is 6.