Question

To make a cup of tea, the ratio of water to milk is 3:2. So to make 5 cups of tea, the ratio of water to milk is:
(a) 4:3:1
(b) 12:1
(c) 15:10
(d) 4:12

Answer 1

Hint: To solve this question, we will, first of all, assume a variable for the given ratio and then by using the unitary method, we will calculate the amount of water and the amount of milk by 5 each separately. Finally, we will calculate the new ratio to get the result.

Complete step-by-step solution:
We are given that to make a cup of tea, the ratio of water to milk is 3:2. We need to determine the ratio of water to milk when 5 cups of tea are to be made. Let the ratio factor be x. To make 1 cup of tea, the ratio is 3:2.
The amount of water for 1 cup of tea = 3x and the amount of milk for 1 cup of tea is 2x.
Now, we will use the unitary method to determine the ratio of 4 cups.
1 cup of tea needs a 3x amount of water.
So, 5 cups of tea need \[3x\times 5\] the amount of water.
So, 5 cups of tea need a 15x amount of water.
Similarly, let’s calculate the amount of milk for 5 cups of tea.
1 cup of tea needs 2x the amount of milk.
So, 5 cups of tea need \[5\times 2x=10x\] the amount of milk.
Let us calculate the ratio for water to milk for 5 cups.
\[\text{Ratio}=\dfrac{\text{Amount of water}}{\text{Amount of milk}}\]
\[\Rightarrow \text{Ratio}=\dfrac{15x}{10x}\]
Cancelling x, we have the ratio as 15:10. Hence to make 5 cups of tea, the ratio of water to milk is 15:10.
Therefore, option (c) is the right answer.

Note: Another method to solve this question can be directly multiplying 5 to both the numerator and denominator of the ratio of water to the milk of 1 cup.
\[\Rightarrow \dfrac{3}{2}\times \dfrac{5}{5}=\dfrac{15}{10}=15:10\]
Hence, we get the same answer.