NCERT Solutions Ganita Prakash (Part 1) Chapter 7 .5 Sharing, but Not Equally! — Figure it Out

Book page 1757 Updated on2026-09-05

Q1.

Divide ₹4,500 into two parts in the ratio 2 : 3.

Answer

₹1,800 and ₹2,700.

Total groups = 2 + 3 = 5
Each group = 4500 ÷ 5 = ₹900
First part = 2 × 900 = ₹1,800
Second part = 3 × 900 = ₹2,700
Check: 1800 + 2700 = 4500 ✓ and 1800 : 2700 = 2 : 3 ✓

Tip: Think of the parts as fractions of the whole — 2⁄5 of ₹4,500 and 3⁄5 of ₹4,500. The two fractions add to 1, which is another way of saying nothing is left over.

Q2.

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?

Answer

40 mL of acid and 200 mL of water.

Total groups = 1 + 5 = 6
Each group = 240 ÷ 6 = 40 mL
Acid = 1 × 40 = 40 mL
Water = 5 × 40 = 200 mL
Check: 40 + 200 = 240 ✓ and 40 : 200 = 1 : 5 ✓

Why 240 is not split into 1 and 5: The ratio 1 : 5 does not mean 1 mL and 5 mL; it means the bottle is made of 6 equal shares, one of acid and five of water. The acid is 1⁄6 of the solution, not 1⁄5 of it — a slip worth guarding against, and in a laboratory a dangerous one.

Q3.

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?

Answer

15 mL of blue and 25 mL of yellow. After adding the yellow, the new ratio is 1 : 3.

Total groups = 3 + 5 = 8
Each group = 40 ÷ 8 = 5 mL
Blue = 3 × 5 = 15 mL Yellow = 5 × 5 = 25 mL

Add 20 mL of yellow: yellow = 25 + 20 = 45 mL, blue is still 15 mL
blue : yellow = 15 : 45, HCF = 15 → 1 : 3

Why the ratio moves so much: Only one term changed. The blue is untouched, so the comparison shifts from 3 : 5 to 1 : 3 — for every part of blue there are now three parts of yellow instead of 1⅔. The total is also up, from 40 mL to 60 mL. Adding to one term of a ratio always changes the ratio; that is precisely how the painter lightens the shade.

Q4.

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?

Answer

4 cups of rice and 2 cups of urad dal.

Total groups = 2 + 1 = 3
Each group = 6 ÷ 3 = 2 cups
Rice = 2 × 2 = 4 cups
Urad dal = 1 × 2 = 2 cups
Check: 4 + 2 = 6 ✓ and 4 : 2 = 2 : 1 ✓

Tip: If you needed 9 cups instead, each group would be 3 cups, giving 6 cups of rice and 3 of dal. The ratio 2 : 1 fixes the recipe; the total decides the size of the batch.

Q5.

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?

Answer

3 : 13.

In one bucket of orange paint:
red = 3⁄8 bucket, yellow = 5⁄8 bucket
Add 1 whole bucket of yellow:
yellow = 5⁄8 + 1 = 13⁄8 bucket, red is unchanged at 3⁄8
red : yellow = 3⁄8 : 13⁄8
Multiply both terms by 8 → 3 : 13

Why no volume in litres is needed: The bucket itself is the unit. Whatever a bucket holds, the orange paint is 3⁄8 red and 5⁄8 yellow, and the added bucket is 1 whole bucket of yellow. Multiplying both terms of 3⁄8 : 13⁄8 by 8 clears the fractions without disturbing the ratio.

Check it yourself: Take the bucket to be 8 litres. Then the orange paint is 3 L red and 5 L yellow; adding 8 L of yellow makes 3 L red to 13 L yellow — the same 3 : 13, as it must be.

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