Question

If 26 horses or 20 bullocks eat up the fodder in store in 170 days, in what time will 10 horses and 8 bullocks finish the same quantity of fodder?

Answer 1

Answer:

216.66 days

Step-by-step explanation:

Let 'h' be the food eaten by the horse per unit time.

Let 'b' be the food eaten by the bullock per unit time.

$26h=\frac{Total\:Food}{170\:Days}$

Therefore, $h=\frac{Total\:Food}{170*26}$

$20b=\frac{Total\:Food}{170\:Days}$

Therefore, $b=\frac{total\:food}{170*20}$

$10h+8b=(10* \frac{T.F.}{170*26} )+(8* \frac{T.F}{170*20} )\\ \\10h+8b=T.F.(\frac{10}{170*26} + \frac{8}{170*20} )\\ \\10h+8b=\frac{T.F.}{170} (\frac{1}{\frac{26}{10} } + \frac{1}{\frac{20}{8} } )\\ \\10h+8b=\frac{T.F.}{170} (\frac{1}{2.6 } + \frac{1}{2.5 } )\\ \\10h+8b=\frac{T.F.}{170} (\frac{5.1}{2.6*2.5 } )\\ \\10h+8b=\frac{T.F.}{ 216.66}$

Answer 2

Answer:

216.66 days

Step-by-step explanation:

Let the total amount of fodder on store be 'x'

Given that 26 horses eat up the fodder in 170 days

=>26 horses eat up 'x/170' amount of fodder in 1 day

=>1 horse will eat up 'x/(170*26)' amount of fodder in 1 day

Now, 10 horse will eat up 'x/(17*26)' amount of fodder in 1 day--(*)

Also,Given that 20 bullocks eat up the fodder in 170 days

=>20 bullocks eat up 'x/170' amount of fodder in 1 day

=>1 bullocks will eat up 'x/(170*20)' amount of fodder in 1 day

Now, 8 bullocks will eat up 'x/425' amount of fodder in 1 day--(**)

=>From (*) and (**),

10 horses and 8 bullocks will eat x/17*26 +x/425 amount of fodder in 1 day

=x/17(1/26 + 1/25)

=3x /650 amount of fodder in 1 day

=>they will finish together the entire fodder 'x' in 650/3 days

= 216.66 days