MathsCBSE Class 10 · Standard · Board exam 2025, set 30/1/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2025: question 32

Set in the CBSE Class 10 board exam of 2025, paper 30/1/1, section D, question 32, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32 · 5 marks · Long answerCompetency-basedPair of Linear Equations in Two Variables

Vijay invested certain amounts of money in two schemes A and B, which offer interest at the rate of 8% per annum and 9% per annum, respectively. He received ₹ 1,860 as the total annual interest. However, had he interchanged the amounts of investments in the two schemes, he would have received ₹ 20 more as annual interest. How much money did he invest in each scheme ?

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/1/1.

Hints

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

Hint 1

Let the amounts in schemes A and B be ₹ $x$ and ₹ $y$ . Write the annual interest from each.

Hint 2

When the amounts are interchanged, $x$ earns 9% and $y$ earns 8%, and the total interest is ₹ 1880.

Hint 3

Add and subtract the two equations to get simple values for $x + y$ and $x - y$ .

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.

Let Vijay invest ₹ $x$ in scheme A (8% p.a.) and ₹ $y$ in scheme B (9% p.a.). Total interest: $\frac{8 x}{100} + \frac{9 y}{100} = 1860$ , so $8 x + 9 y = 186000$ ...(i)
1½ marks
If the amounts are interchanged, the interest is $1860 + 20 = 1880$ . So $\frac{9 x}{100} + \frac{8 y}{100} = 1880$ , which gives $9 x + 8 y = 188000$ ...(ii)
1½ marks
Adding (i) and (ii): $17 x + 17 y = 374000$ , so $x + y = 22000$ ...(iii). Subtracting (i) from (ii): $x - y = 2000$ ...(iv). Adding (iii) and (iv): $2 x = 24000$ , so $x = 12000$ .
1 mark
From (iii): $y = 22000 - 12000 = 10000$ . Check: $960 + 900 = 1860$ and $1080 + 800 = 1880$ . Hence Vijay invested ₹ 12000 in scheme A and ₹ 10000 in scheme B.
1 mark

Answer: Scheme A: ₹ 12,000; Scheme B: ₹ 10,000

Where the marks are

Forms the first equation $8 x + 9 y = 186000$ (1½ marks)
Forms the second equation $9 x + 8 y = 188000$ (1½ marks)
Solves to get $x = 12000$ (1 mark)
Gets $y = 10000$ and states both investments (1 mark)

Revise the chapter

Chapter: Pair of Linear Equations in Two Variables (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Pair of Linear Equations in Two Variables, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 30/1/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 32

Hints

Step-by-step solution

Revise the chapter

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