Figure it Out — Sharing in a Given Ratio — Proportional Reasoning

1. 12 marksGanita Prakash Cl-8 Part 1, Figure it Out, page 175

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

   Hint. Add the parts of the ratio to find how many equal shares the total must be split into.

   Step 1 — Find the total number of shares. The ratio 2 : 3 means the money is split into 2 + 3 = 5 equal shares.

   Step 2 — Find the value of one share. One share = ₹4,500 ÷ 5 = ₹900

   Step 3 — Build each part. First part = 2 shares = 2 × 900 = ₹1,800 Second part = 3 shares = 3 × 900 = ₹2,700

   Step 4 — Check both conditions. • They add back to the total: 1800 + 2700 = 4500 ✓ • They are in the right ratio: 1800 : 2700 = 18 : 27 = 2 : 3 ✓

   Both checks matter. Getting the ratio right but the total wrong (say ₹2,000 and ₹3,000) is a common slip, and so is splitting the total correctly but in the wrong order.

   The general method, worth memorising because every question in this set uses it: to divide an amount T in the ratio a : b, each share is T ÷ (a + b), and the parts are a/(a+b) × T and b/(a+b) × T. Here that is (2/5) × 4500 = 1800 and (3/5) × 4500 = 2700 ✓

   ✦ ₹1,800 and ₹2,700 — the total splits into 5 shares of ₹900 each.

2. 22 marksGanita Prakash Cl-8 Part 1, Figure it Out, page 175

   In a science lab, acid and water are mixed in the ratio 1 : 5 to make a solution. In a bottle holding 240 mL of the solution, how much acid and how much water does it contain?

   Hint. The ratio 1 : 5 means the whole solution is 6 parts, not 5.

   Step 1 — Count the total parts. Acid : water = 1 : 5, so the solution consists of 1 + 5 = 6 parts in all.

   This is where mistakes happen. The ratio 1 : 5 does not mean the acid is one-fifth of the solution — it means acid is one part out of six, so one-sixth.

   Step 2 — Find one part. One part = 240 mL ÷ 6 = 40 mL

   Step 3 — Find each quantity. Acid = 1 part = 40 mL Water = 5 parts = 5 × 40 = 200 mL

   Step 4 — Check. • Total: 40 + 200 = 240 mL ✓ • Ratio: 40 : 200 = 1 : 5 ✓

   By fractions: acid = (1/6) × 240 = 40 mL and water = (5/6) × 240 = 200 mL ✓

   A practical note. In a real laboratory, acid is always added to water and never the other way round, because the mixing releases heat and can make the acid spit. The mathematics is unaffected, but the order matters.

   ✦ 40 mL of acid and 200 mL of water — the solution is 6 parts in total, each of 40 mL.

3. 33 marksGanita Prakash Cl-8 Part 1, Figure it Out, page 175

   Blue and yellow paints are mixed in the ratio 3 : 5 to produce green paint. To produce 40 mL of green paint, how much of each colour is needed? To make a lighter shade, 20 mL of yellow is then added. What is the new ratio of blue to yellow?

   Hint. For the second part, only the yellow changes — the blue stays exactly as it was.

   Part 1 — Making the 40 mL.

   The ratio 3 : 5 gives 3 + 5 = 8 parts in total. One part = 40 mL ÷ 8 = 5 mL

   Blue = 3 parts = 3 × 5 = 15 mL Yellow = 5 parts = 5 × 5 = 25 mL

   Check: 15 + 25 = 40 mL ✓ and 15 : 25 = 3 : 5 ✓

   Part 2 — After adding 20 mL of yellow.

   Only the yellow changes, because nothing was done to the blue: Blue = 15 mL (unchanged) Yellow = 25 + 20 = 45 mL

   New ratio = 15 : 45 Dividing both parts by their HCF, 15: = 1 : 3

   Check: the total is now 60 mL, and 1 : 3 of 60 mL is 15 mL and 45 mL ✓

   Why the shade gets lighter. Blue has gone from three-eighths of the mixture to only one-quarter, so yellow now dominates more strongly — which is exactly what produces a lighter green.

   The error to avoid: adding 20 to both parts of 3 : 5, or adjusting the blue to keep the total at 40 mL. The question adds yellow to the existing mixture, so the blue quantity is untouched and the total simply grows.

   ✦ 15 mL blue and 25 mL yellow; after adding 20 mL more yellow the ratio becomes 15 : 45 = 1 : 3.

4. 42 marksGanita Prakash Cl-8 Part 1, Figure it Out, page 175

   To make soft idlis you need rice and urad dal in the ratio 2 : 1. If you need 6 cups of this mixture, how many cups of rice and urad dal will you need?

   Hint. Two parts rice to one part dal means three parts altogether.

   Step 1 — Work out how many equal shares the mixture holds. Rice : dal = 2 : 1, so the mixture has 2 + 1 = 3 parts.

   Step 2 — Find one part. One part = 6 cups ÷ 3 = 2 cups

   Step 3 — Find each quantity. Rice = 2 parts = 2 × 2 = 4 cups Urad dal = 1 part = 2 cups

   Step 4 — Check. • Total: 4 + 2 = 6 cups ✓ • Ratio: 4 : 2 = 2 : 1 ✓

   Reading the ratio correctly. "Rice and urad dal in the ratio 2 : 1" means there is twice as much rice as dal — so rice must be the larger of the two answers. If your rice figure comes out smaller than your dal figure, the ratio has been applied the wrong way round.

   Scaling the recipe. Because this is a ratio, the recipe scales freely: 12 cups of mixture would need 8 cups of rice and 4 of dal; 3 cups would need 2 and 1. The proportion of rice to dal — and hence the texture of the idlis — stays the same at every scale.

   ✦ 4 cups of rice and 2 cups of urad dal — the mixture is 3 parts in total, each of 2 cups.

5. 53 marksGanita Prakash Cl-8 Part 1, Figure it Out, page 175

   I have one bucket of orange paint made by mixing red and yellow in the ratio 3 : 5. I add another full bucket of yellow paint to this mixture. What is the ratio of red to yellow in the new mixture?

   Hint. Work in units of buckets. How much of the first bucket is red, and how much is yellow?

   Step 1 — Express the first bucket in fractions of a bucket. Red : yellow = 3 : 5 gives 8 parts in total, so within that one bucket Red = 3/8 of a bucket Yellow = 5/8 of a bucket

   Working in buckets rather than millilitres is the key move here, because no actual volume is given — only "one bucket".

   Step 2 — Add the extra yellow. A whole bucket of yellow is added, so Red = 3/8 (unchanged) Yellow = 5/8 + 1 = 5/8 + 8/8 = 13/8 of a bucket

   Step 3 — Form the new ratio. Red : yellow = 3/8 : 13/8

   Both sides share the denominator 8, so multiplying through by 8 clears it: = 3 : 13

   Step 4 — Sanity check. There are now 2 buckets of paint altogether, and 3 + 13 = 16 parts. So one part is 2/16 = 1/8 of a bucket, making the red 3/8 of a bucket ✓ — matching where we started.

   The common error is to say "add one to the yellow part of 3 : 5" and write 3 : 6. That treats the added bucket as if it were a single part, but a whole bucket is 8 parts, not 1.

   ✦ 3 : 13 — the red stays at 3/8 of a bucket while the yellow rises from 5/8 to 13/8.

Solutions written by the tuition.in editorial team and checked against the NCERT Class 8 Mathematics textbook Ganita Prakash Part 1, Reprint 2026-27 (hegp107.pdf). Four 'Figure it Out' blocks sit on pages 165, 170, 175 and 176-178. Every numeric answer here was independently recomputed before comparison with the book's printed answer key — including the acre-to-square-feet conversions (1 acre = 43,560 sq ft), the Lilavati saffron problem, the population densities of Delhi and Mumbai, and the cupro-nickel coin costings. THREE NOTES ARE FLAGGED IN PLACE: (1) question 6 on page 165 depends on counting bricks in a printed pattern, so its counts are cited from the key rather than derived; (2) questions 4, 5 and 7 on page 165 are measurement and drawing activities with no single numeric answer — the method is given instead; (3) the printed key's working for question 2 on page 176 contains a garbled fraction ('x = 34/9'), so the solution is re-derived cleanly here while reaching the same final answer of 4 buses.. Questions are referenced from the NCERT textbook for identification.