Figure it Out — Inverse Proportion Tables — Proportional Reasoning-2

1. 13 marksGanita Prakash Cl-8 Part 2, Figure it Out, page 65

   Which of these are in inverse proportion? (i) x = 40, 80, 25, 16 with y = 20, 10, 32, 50 (ii) x = 40, 80, 25, 16 with y = 20, 10, 12.5, 8 (iii) x = 30, 90, 150, 10 with y = 15, 5, 3, 45

   Hint. For inverse proportion the product xy must be the same in every column — test all of them, not just the first two.

   The test. Quantities x and y are in inverse proportion when xy = k for a constant k. So multiply each column and see whether one number comes out every time.

   (i) 40 × 20 = 800 · 80 × 10 = 800 · 25 × 32 = 800 · 16 × 50 = 800 All four products are 800, so this table is in inverse proportion, with k = 800.

   (ii) 40 × 20 = 800 · 80 × 10 = 800 · 25 × 12.5 = 312.5 · 16 × 8 = 128 The first two columns agree, but the third and fourth do not, so this table is not in inverse proportion.

   (iii) 30 × 15 = 450 · 90 × 5 = 450 · 150 × 3 = 450 · 10 × 45 = 450 All four products are 450, so this table is in inverse proportion, with k = 450.

   Why (ii) is the interesting one — check every column. Its first two columns are identical to those of (i), so anyone who tests only the start of the table will call it inverse and be wrong. A single mismatched column is enough to break the relationship.

   And (ii) is not directly proportional either. For a direct proportion the quotients would have to match: 40/20 = 2, but 80/10 = 8. So the table shows neither kind of proportion — it is simply four unrelated pairs.

   ✦ (i) and (iii) are in inverse proportion, with constants 800 and 450. (ii) is not — its last two columns give products 312.5 and 128 instead of 800 — and it is not directly proportional either.

2. 23 marksGanita Prakash Cl-8 Part 2, Figure it Out, page 65

   Fill in the empty cells if x and y are in inverse proportion: x = 16, 12, ___, 36 and y = 9, ___, 48, ___

   Hint. One column is complete. Use it to find the constant, then work every other cell from that constant.

   Find the constant from the one complete column. The first column is the only one with both values filled in, so it is the one that fixes the constant: k = x × y = 16 × 9 = 144 Every other column must have this same product, because that is what inverse proportion means.

   Second column — x = 12, find y. 12 × y = 144 y = 144 ÷ 12 = 12

   Third column — y = 48, find x. x × 48 = 144 x = 144 ÷ 48 = 3

   Fourth column — x = 36, find y. 36 × y = 144 y = 144 ÷ 36 = 4

   The completed table:

   x	16	12	3	36
   y	9	12	48	4

   Check every column. 16 × 9 = 144 · 12 × 12 = 144 · 3 × 48 = 144 · 36 × 4 = 144 ✓

   Notice the behaviour. As x falls from 16 to 12 to 3, y climbs from 9 to 12 to 48 — the two move in opposite directions, exactly as inverse proportion demands. And when x jumps from 3 to 36, twelve times larger, y drops from 48 to 4, twelve times smaller.

   ✦ x = 16, 12, 3, 36 and y = 9, 12, 48, 4, with the constant product xy = 144.

Solutions written by the tuition.in editorial team and checked against the NCERT Class 8 Mathematics textbook Ganita Prakash Part 2, Reprint 2026-27 (hegp203.pdf), where this is Chapter 3 (pages 55-69) — the tenth chapter of the Class 8 course. Like the rest of Part 2, this PDF carries NO printed answer key, so every answer was derived from first principles and independently recomputed in Python before being written. TWO FIGURE-ONLY ITEMS WERE RESOLVED BY MEASURING THE RENDERED PAGE rather than guessing: (1) the eight sleep ring charts on page 67 were rendered at 300 dpi and the shaded arc of each ring measured by sampling 3600 points around its circumference — the eight measured fractions map one-to-one onto the eight values the question offers (giraffe 2.96 -> 2.5, elephant 3.84 -> 3.5, human 7.78 -> 8, dog 10.07 -> 10.5, cat 12.99 -> 13, squirrel 15.08 -> 15, python 18.09 -> 18, bat 20.16 -> 20), which is what fixes the assignment; (2) the transport pie chart on page 68 prints only four of its five angles, so the page was rendered and the labels read off before deducing Car = 30 degrees. ONE ITEM IS FLAGGED AS UNANSWERABLE FROM THE PDF: the map distances in section 3.2, because the chapter PDF stamps its map 'Map not to scale' - the method is given and no distance is invented. ONE APPARENT SLIP IN THE BOOK IS FLAGGED: page 68 question 5(iii) asks how many children use 'taxis', but taxi is not one of the five modes in the pie chart and the five slices already total 360 degrees, so the answer as printed is zero; the solution says so and notes that 'two-wheeler' (36 children) was probably intended.. Questions are referenced from the NCERT textbook for identification.