Saving money is a good habit and it should be inculcated in children right from the beginning. Rehan's mother brought a piggy bank for Rehan and puts one ₹ 5 coin of her savings in the piggy bank on the first day. She increases his savings by one ₹ 5 coin daily. Based on the above information, answer the following questions: (i) How many coins were added to the piggy bank on 8th day? (ii) How much money will be there in the piggy bank after 8 days? (iii) (a) If the piggy bank can hold one hundred twenty ₹ 5 coins in all, find the number of days she can contribute to put ₹ 5 coins into it. (iii) (b) Find the total money saved, when the piggy bank is full.

MathsCBSE Class 10 · Basic · Board exam 2024, set 430/2/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Basic 2024: question 36

Set in the CBSE Class 10 board exam of 2024, paper 430/2/1, 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

Saving money is a good habit and it should be inculcated in children right from the beginning. Rehan's mother brought a piggy bank for Rehan and puts one ₹ 5 coin of her savings in the piggy bank on the first day. She increases his savings by one ₹ 5 coin daily.

Based on the above information, answer the following questions:

(i)
How many coins were added to the piggy bank on 8th day?
1 mark
(ii)
How much money will be there in the piggy bank after 8 days?
1 mark
(iii) (a)
If the piggy bank can hold one hundred twenty ₹ 5 coins in all, find the number of days she can contribute to put ₹ 5 coins into it.
2 marks
OR
(iii) (b)
Find the total money saved, when the piggy bank is full.
2 marks

Figure in the paper: Photograph of a pink piggy bank on the left, with a hand dropping a coin into it; to the right, stacks of coins of decreasing height, representing the savings increasing day by day (the stacks shown get progressively shorter from left to right). See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/2/1.

Hints

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

Hint 1

Write down how many coins go in on day 1, day 2, day 3… — what kind of sequence is this?

Hint 2

For the total after some days, use $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$ ; remember each coin is worth ₹5.

Hint 3

For (iii)(a), set the total number of coins equal to 120 and solve the quadratic in $n$ , keeping only the positive root.

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.

(i) She puts 1 coin on day 1 and one more coin each day, so coins added on successive days are $1, 2, 3, \dots$ (AP with $a = 1, d = 1$ ).
Coins on 8th day $= a_{8} = 1 + 7 (1) = 8$ coins
1 mark
(ii) Money added day-wise: ₹5, ₹10, ₹15, ₹20, … (AP with $a = 5, d = 5$ ).
$S_{8} = \frac{8}{2} [2 (5) + 7 (5)] = 4 \times 45 = ₹180$
1 mark
(iii)(a) Total coins in $n$ days $= \frac{n}{2} [2 (1) + (n - 1) (1)]$ . The bank holds 120 coins, so
$\frac{n}{2} [2 + (n - 1)] = 120$
1 mark
$\Rightarrow n (n + 1) = 240 \Rightarrow n^{2} + n - 240 = 0$
½ mark
$\Rightarrow (n + 16) (n - 15) = 0 \Rightarrow n = 15$ (since $n \neq = - 16$ , days cannot be negative).
She can contribute for 15 days.
½ mark
(iii)(b) When full, the bank holds 120 coins of ₹5 each.
Total money saved $= 120 \times 5$
1 mark
$= ₹600$
1 mark

Answer: (i) 8 coins; (ii) ₹180; (iii)(a) 15 days; (iii)(b) ₹600

Where the marks are

(i) 8 coins on the 8th day (1 mark)
(ii) Money after 8 days = ₹180 (1 mark)
(iii)(a) Sets up $\frac{n}{2} [2 + (n - 1)] = 120$ (1 mark)
(iii)(a) Obtains $n^{2} + n - 240 = 0$ (½ mark)
(iii)(a) Solves to get $n = 15$ , rejecting $- 16$ (½ mark)
(iii)(b) Total money $= 120 \times 5 = ₹600$ (1 + 1 marks)

Revise the chapter

Chapter: Arithmetic Progressions (notes, formulas, where marks are lost and every past question)
Topic: Finding nth Term from the Sum of n Terms

Practise this chapterBoard-style questions from Arithmetic Progressions, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 430/2/1 (Basic): 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 Basic 2024: question 36

Hints

Step-by-step solution

Revise the chapter

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