Question

30. The prices of two varieties of pulses X and Y are $20/kg and $25/kg respectively. What ratio of X:Y should be mixed to get a mixture worth $21.50?

Answer 1

Step-by-step explanation:

The prices of two varieties of pulses X and Y are $20/kg and $25/kg respectively. What ratio of X:Y should be mixed to get a mixture worth $21.50?

Answer 2

Given:

Cost of X variety of pulses = $20/kg

Cost of Y variety of pulses = $25/kg

To find:

The ratio to mix X and Y to get a mixture worth $21.50

Solution:

Let $a$ be the amount of variety X in the mixture worth $21.50.

Let $b$ be the amount of variety Y in the mixture worth $21.50.

Amount of both varieties = $a+b$

Individual cost of both varieties in the mixture = $20a+25b$

where $20 is the cost of 1kg of X variety and $25 is the cost of 1kg of Y variety.

But, total price of the mixture = $21.50

Hence, total cost of both varieties = $21.50(a+b)$

Therefore, in equation form,

$21.50(a+b)=20a+25b$

$21.50a+21.50b=20a+25b$

$21.50a-20a=25b-21.50b$

$1.5a=3.5b$

$\frac{a}{b}=\frac{3.5}{1.5}=\frac{7}{3}$

Thus, the ratio is 7:3.

The ratio in which variety X and variety Y of the pulses should be mixed to get a mixture worth $21.50 is 7:3.