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Ratio

by vaibhav101 » Wed Aug 01, 2018 7:47 am

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A certain farm has group of sheep , some of which are Rams( males) and the rest ewes(females). The ratio of Rams to ewes on the farms is 4 to 5. The sheep are divided into 3 pens,each of which same number of sheep. If the ratio of Rams to ewes in the first pen is 4 to 11, and if the ratio of Rams to ewes is equal in the second and third pen, which of the following is the ratio of Rams in the third pen?

A 8/7
B 2/3
C 1/2
D3/12
E 1/6
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by deloitte247 » Sat Aug 11, 2018 6:14 am
The ratio of rams to ewes on the farm is 4 to 5, hence we have;
Rams : Ewes = 4x : 5x
Total sheep = 9x
The sheep are divided into three pens, each of which contains the same number of sheep.
Therefore, each pen contains 3x sheep.
Ratio of rams to ewes in the first pen is 4 to 11,
That is 4y : 11y
Sheep in the first pen = 15y
Each pen contains 3x sheep,
Thus, 3x = 15y
x = 5y
From ram : ewes as 4x : 5x (substituting)(x = 5y)
= 4 (5y) : 5 (5y)
= 20y : 25y
Together in the second pen we have
20y - 4y = 16y rams and
25y - 11y = 14y ewes.
So 8y rams and 7y ewes in each.
In the ratio 8y : 7y
$$=\ 8\ :\ 7\ =\ \frac{8}{7}$$
Option A is CORRECT.
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