Case Study – 1 Your elder brother wants to buy a car and plans to take a loan from a bank for his car. He repays his total loan of ₹ 1,18,000 by paying every month, starting with the first instalment of ₹ 1,000 and he increases the instalment by ₹ 100 every month. Based on the information given above, answer the following questions : (i) Find the amount paid by him in the 30th instalment. (ii) If the total number of instalments is 40, what is the amount paid in the last instalment? (iii)(a) What amount does he still have to pay after the 30th instalment? (iii)(b) Find the ratio of the tenth instalment to the last instalment.

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/2/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2026: question 36

Set in the CBSE Class 10 board exam of 2026, paper 30/2/1, section E, question 36, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q36 · 4 marks · Case-basedCompetency-basedArithmetic Progressions

Case Study – 1

Your elder brother wants to buy a car and plans to take a loan from a bank for his car. He repays his total loan of ₹ 1,18,000 by paying every month, starting with the first instalment of ₹ 1,000 and he increases the instalment by ₹ 100 every month.

Based on the information given above, answer the following questions :

(i)
Find the amount paid by him in the 30th instalment.
1 mark
(ii)
If the total number of instalments is 40, what is the amount paid in the last instalment?
1 mark
(iii)(a)
What amount does he still have to pay after the 30th instalment?
2 marks
OR
(iii)(b)
Find the ratio of the tenth instalment to the last instalment.
2 marks

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/2/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

The instalments go up by the same amount each month. What kind of sequence is that?

Hint 2

Use $a_{n} = a + (n - 1) d$ for a single instalment and $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$ for the total paid so far.

Hint 3

For (iii)(a), the amount still owed is the total loan minus the sum of the first 30 instalments.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

The instalments form an A.P.: $1000, 1100, 1200, \dots$ with first term $a = 1000$ and common difference $d = 100$ .
(i) $a_{30} = a + 29 d = 1000 + 29 (100) = 3900$ . So the 30th instalment is ₹ 3900.
1 mark
(ii) $a_{40} = a + 39 d = 1000 + 39 (100) = 4900$ . So the last (40th) instalment is ₹ 4900.
1 mark
(iii)(a) Amount paid in the first 30 instalments: $S_{30} = \frac{30}{2} [2 (1000) + 29 (100)] = 15 \times 4900 = 73500$ , i.e. ₹ 73500.
1 mark
(iii)(a) Amount still to be paid $= 118000 - 73500 = ₹ 44500$ .
1 mark
(iii)(b) $a_{10} = 1000 + 9 (100) = 1900$ and $a_{40} = 4900$ , so $\frac{a _{10}}{a _{40}} = \frac{1900}{4900}$ .
1 mark
(iii)(b) $\frac{1900}{4900} = \frac{19}{49}$ , so the ratio is $19 : 49$ .
1 mark

Answer: (i) ₹ 3900; (ii) ₹ 4900; (iii)(a) ₹ 44500; (iii)(b) 19 : 49

Where the marks are

Uses $a_{n} = a + (n - 1) d$ with $a = 1000$ , $d = 100$ to get $a_{30} = 3900$ (1 mark)
Finds $a_{40} = 4900$ (1 mark)
(iii)(a) Finds $S_{30} = 73500$ (1 mark)
(iii)(a) Subtracts from 118000 to get ₹ 44500 (1 mark)
(iii)(b) Writes $a_{10} / a_{40} = 1900/4900$ (1 mark)
(iii)(b) Simplifies to 19 : 49 (1 mark)

Revise the chapter

Chapter: Arithmetic Progressions (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Arithmetic Progressions, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/2/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard 2026: question 36

Hints

Step-by-step solution

Revise the chapter

More questions from Arithmetic Progressions