Mr Kumar had 6 of brown paint and 10.05 ℓ of black paint. He poured out 6 cups of paint for each colour to paint his bookshelf. In the end. there was 2/5 as black paint.
(a) How many litres of paint did he use for each colour?
(b) What was the capacity of the cup?
First, let's calculate the total amount of paint Mr Kumar had:
Total amount of brown paint = 6 cups * 6ℓ/cup = 36ℓ
Total amount of black paint = 10.05ℓ
Next, let's calculate how much black paint remained after pouring out 6 cups:
Remaining black paint = 10.05ℓ - 6 cups = 10.05ℓ - 6 * 6ℓ/cup = 10.05ℓ - 36ℓ = -25.95ℓ
Since the remaining black paint is negative, it means that there is not enough black paint, and the total paint used is less than 2/5 of the bookshelf.
(a) Since there is not enough black paint, we can't calculate how much paint was used for each color.
(b) The capacity of the cup cannot be determined based on the information given.
To solve this problem, we can use ratios and proportions. Let's first find out how much paint Mr Kumar used for each color.
(a) How many liters of paint did he use for each color?
Given:
Brown paint = 6 cups
Black paint = 6 cups
Let's assume the total amount of paint Mr Kumar used for both colors is "x liters".
So, using ratios, we can write:
Brown paint used / Total paint used = Brown paint cups / Total cups of paint
Black paint used / Total paint used = Black paint cups / Total cups of paint
For brown paint:
6 cups / x liters = 6 cups / (6 cups + 6 cups)
Simplifying the equation:
6 / x = 6 / 12
6x = 6 * 12
6x = 72
x = 72 / 6
x = 12
So, Mr Kumar used 12 liters of paint for each color.
(b) What was the capacity of the cup?
To find the capacity of the cup, we need to divide the total amount of paint used by the number of cups used.
For brown paint:
12 liters / 6 cups = 2 liters/cup
For black paint:
12 liters / 6 cups = 2 liters/cup
Therefore, the capacity of the cup was 2 liters.
In conclusion:
(a) Mr Kumar used 12 liters of paint for each color.
(b) The capacity of the cup was 2 liters.