Question

pls solve it very important

Answer 1

let time taken by one man alone be x and time taken by one boy alone be y.
one man one day's work =1/x
one boy one day's work =1/y

According to the question...

case 1...
4/x+6/y = 1/5

case 2...
3/x +4/y =1/7

now, let 1/x be a and 1/y be b

4a + 6b =1/5
3a +4b =1/7

(4a +6b =1/5)3
(3a + 4b =1/7)4

12a +18b = 3/5.....(1)
12a + 16b=4/7......(2)
subtracting (2) from (1)...

12a + 18b -(12a +16b) =3/5-4/7
12a+18b-12a-16b=3/5-4/7
2b=3/5-4/7
$2b = \frac{21 - 20}{35} \\ 2b = \frac{1}{35} \\ b = \frac{1}{70} \\ \frac{1}{y} = \frac{1}{70 } \\ y = 70 \: days$


3a +4b =1/7
$3a + \frac{2}{35} = \frac{1}{7} \\ 3a = \frac{5 - 2}{35} \\ 3a = \frac{3}{35} \\ a = \frac{1}{35}$
$a = \frac{1}{35} \\ \frac{1}{x} = \frac{1}{35} \\ x = 35 days$
hence, x=35 days, and
y=70 days