NCERT Solutions for Class 8 Maths Ganita Prakash Chapter 7 — Figure it Out (Page 175)#
To divide a quantity $x$ in the ratio $m : n$, split it into $m + n$ equal parts:
- first share $= \dfrac{m}{m + n} \times x$
- second share $= \dfrac{n}{m + n} \times x$
1. Divide ₹4,500 into two parts in the ratio 2 : 3. #
Solution
There are $2 + 3 = 5$ equal parts.
First part $= \dfrac{2}{5} \times 4500$
First part $= 1800$
Second part $= \dfrac{3}{5} \times 4500$
Second part $= 2700$
Check: $1800 + 2700 = 4500$ and $1800 : 2700 = 2 : 3$.
∴ The two parts are ₹1,800 and ₹2,700.
2. In a science lab, acid and water are mixed in the ratio of 1 : 5 to make a solution. In a bottle that has 240 mL of the solution, how much acid and water does the solution contain? #
Solution
There are $1 + 5 = 6$ equal parts.
Acid $= \dfrac{1}{6} \times 240$
Acid $= 40$ mL
Water $= \dfrac{5}{6} \times 240$
Water $= 200$ mL
∴ The solution contains 40 mL of acid and 200 mL of water.
3. Blue and yellow paints are mixed in the ratio of 3 : 5 to produce green paint. To produce 40 mL of green paint, how much of these two colours are needed? To make the paint a lighter shade of green, I added 20 mL of yellow to the mixture. What is the new ratio of blue and yellow in the paint? #
Solution
There are $3 + 5 = 8$ equal parts.
Blue $= \dfrac{3}{8} \times 40$
Blue $= 15$ mL
Yellow $= \dfrac{5}{8} \times 40$
Yellow $= 25$ mL
After adding 20 mL of yellow:
Yellow $= 25 + 20$
Yellow $= 45$ mL
Blue : yellow $= 15 : 45$
Blue : yellow $= 1 : 3$
∴ We need 15 mL of blue and 25 mL of yellow, and the new ratio is 1 : 3.
4. To make soft idlis, you need to mix rice and urad dal in the ratio of 2 : 1. If you need 6 cups of this mixture to make idlis tomorrow morning, how many cups of rice and urad dal will you need? #
Solution
There are $2 + 1 = 3$ equal parts.
Rice $= \dfrac{2}{3} \times 6$
Rice $= 4$ cups
Urad dal $= \dfrac{1}{3} \times 6$
Urad dal $= 2$ cups
∴ You need 4 cups of rice and 2 cups of urad dal.
5. I have one bucket of orange paint that I made by mixing red and yellow paints in the ratio of 3 : 5. I added another bucket of yellow paint to this mixture. What is the ratio of red paint to yellow paint in the new mixture? #
Solution
Take one bucket as 1 unit of paint. The orange paint is $\dfrac{3}{8}$ red and $\dfrac{5}{8}$ yellow.
Red $= \dfrac{3}{8}$ bucket
After adding one whole bucket of yellow:
Yellow $= \dfrac{5}{8} + 1$
Yellow $= \dfrac{13}{8}$ bucket
Red : yellow $= \dfrac{3}{8} : \dfrac{13}{8}$
Red : yellow $= 3 : 13$
∴ The new ratio of red to yellow is 3 : 13.
(Another way: think of the bucket as 8 cups, 3 red and 5 yellow. Adding 8 cups of yellow gives 3 red and 13 yellow.)