NCERT Solutions for Class 7th Maths Chapter 7 Solving Problems — In-text Questions
Book page 174 – 175 Updated on2026-09-19
Q1.
Example 7: Ranjana creates a sequence of arrangements with square tiles as shown below. Can she extend the sequence and make an arrangement using 100 tiles? If yes, which step in the sequence will it be?The first three steps of Ranjana’s sequence of square tiles.
Answer
Yes — it will be Step 33.
First get the rule. The book shows two ways of seeing the same pattern.
Why it happens: both ways of looking at the picture give the same expression, 3k + 1, which is a good sign that the rule is right. Since 33 is a whole number, Step 33 really exists, so the arrangement can be made. Had the division not come out exact, the answer would have been "no".
Check it yourself: 3 × 33 + 1 = 99 + 1 = 100. ✓
Q2.
To check whether an arrangement is possible using 100 tiles at some Step k, we can solve the equation: 3k + 1 = 100. Find the value of k.
Answer
k = 33.
3k + 1 = 100
3k + 1 − 1 = 100 − 1 (remove the term 1 from both sides)
3k = 99
3k ÷ 3 = 99 ÷ 3 (remove the factor 3)
k = 33
Why it happens: the same two moves as always — first the term, then the factor. The answer being a whole number is what makes the arrangement possible. If we had asked about 101 tiles we would get 3k = 100, and 100 is not divisible by 3, so no step of the sequence uses 101 tiles.
Try This: which nearby numbers of tiles are possible? 3k + 1 gives 4, 7, 10, 13, … — every number that leaves remainder 1 on division by 3.