NCERT Solutions for Class 7th Maths Chapter 4 Formula Detective — Pick Patterns and Reveal Relationships
Book page 95–96 Updated on2026-09-19
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.
The five number machines, page 95 — each takes the two numbers at the top of the ‘Y’ and produces the result at the bottom.
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.