NCERT Solutions Ganita Prakash (Part 1) Chapter 4 –96Section 4.5 Pick Patterns and Reveal Relationships — Formula Detective

Book page 95 Updated on2026-09-05

Q1.

Look at the picture given. In each case, the number machine takes in the 2 numbers at the top of the ‘Y’ as inputs, performs some operations and produces the result at the bottom. Find out the formula of this number machine. (inputs and outputs: 5, 2 → 8; 8, 1 → 15; 9, 11 → 7; 10, 10 → 10; 6, 4 → ?)

Answer

The formula is “two times the first number minus the second number”, that is 2a – b.

Inputs (a, b)	Expression	Output
5, 2	2 × 5 – 2	8
8, 1	2 × 8 – 1	15
9, 11	2 × 9 – 11	7
10, 10	2 × 10 – 10	10
6, 4	2 × 6 – 4	8

Why it happens: One example is never enough — 5 and 2 also fit “a + b + 1”. Testing the rule on every pair is what confirms 2a – b.

Q2.

Find the formulas of the number machines below and write the expression for each set of inputs. (Machine 1: 5, 2 → 5; 8, 1 → 7; 9, 11 → 18; 10, 10 → 18; a, b → ? Machine 2: 4, 1 → 5; 6, 0 → 1; 3, 2 → 7; 10, 3 → ?; a, b → ?)

Answer

Machine 1 — “add the two numbers, then subtract 2”, that is a + b – 2.

Inputs	Expression	Output
5, 2	5 + 2 – 2	5
8, 1	8 + 1 – 2	7
9, 11	9 + 11 – 2	18
10, 10	10 + 10 – 2	18
a, b	a + b – 2	a + b – 2

Machine 2 — “multiply the two numbers, then add 1”, that is ab + 1.

Inputs	Expression	Output
4, 1	4 × 1 + 1	5
6, 0	6 × 0 + 1	1
3, 2	3 × 2 + 1	7
10, 3	10 × 3 + 1	31
a, b	a × b + 1	ab + 1

Tip: The pair (6, 0) is the giveaway for Machine 2. Any rule that only added would give 6 or 7; only multiplying can crush 6 down to 1.

Q3.

Now, make a formula on your own. Write a few number machines as examples using that formula. Challenge your classmates to figure it out!

Answer

Here is one you can use. Formula: 3a – 2b — “three times the first number minus twice the second”.

Inputs (a, b)	Working	Output
4, 1	3 × 4 – 2 × 1	10
5, 5	3 × 5 – 2 × 5	5
2, 3	3 × 2 – 2 × 3	0
7, 2	3 × 7 – 2 × 2	17
1, 4	3 × 1 – 2 × 4	–5

Try This: Include one pair that gives 0 and one that gives a negative answer, as above. Those two cases make guessing much harder — and much more fun.

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