Question

if 4 goats or 6 sheep can graze a field in 40 days, how many days will 4 goats and 14 sheep take to graze the same field show all steps of the sum

Answer 1

4 goats= 6 sheep
:-total work=6×40 days
=4 goats and 14 sheep can complete work in
a/q 4 goats= 6 sheep
6 sheep + 14 sheep= 20 sheep do same work in 6 × 40 total work by 20 sheep
240÷20 =12 days ans....

Answer 2

Given:

4 goats or 6 sheep can graze a field in 40 days

To Find:

how many days will 4 goats and 14 sheep take to graze the same field

Solution:

we can solve this question using the formula

$\frac{M_{1}D_{1}H_{1}}{W_{1}} =\frac{M_{2}D_{2}H_{2}}{W_{2}}$

But before using this formula lets Find the value of 4 goats and 14 sheep in only terms of goats

It is given that 4 goats are equal to 6 sheep as they both can do the same work at the same time so,

$4G=6S\\S=\frac{2}{3}G$

Now putting this value in 4 goats and 14 sheep equation

$=4G+14S\\=4G+14*\frac{2}{3}G\\=\frac{40}{3}G$

Now we can use the formula to find the amount of time it will take

$4G*40Days=\frac{40}{3}G*x\\x=12days$

Hence, it will take 12 days for 4 goats and 14 sheep to graze the same field.