MathsCBSE Class 10 · Standard · Board exam 2026, set 30/1/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2026: question 35

Set in the CBSE Class 10 board exam of 2026, paper 30/1/1, section D, question 35, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q35 · 5 marks · Long answerStatistics

The mean of the following frequency distribution is 35. Find the values of $x$ and $y$ , if the sum of frequencies is 25 :

Class	Frequency
0-10	1
10-20	$x$
20-30	5
30-40	7
40-50	$y$
50-60	3
60-70	1

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

Hints

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

Hint 1

Find the class marks and make an $f_{i} x_{i}$ column.

Hint 2

Use $\sum f_{i} = 25$ to get one equation in $x$ and $y$ .

Hint 3

Use mean $= \sum f_{i} x_{i} / \sum f_{i} = 35$ for the second equation, then solve the pair.

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.

Take the class marks $x_{i}$ and find $f_{i} x_{i}$ for each class:
Class $f_{i}$ $x_{i}$ $f_{i} x_{i}$
0-10 1 5 5
10-20 $x$ 15 $15 x$
20-30 5 25 125
30-40 7 35 245
40-50 $y$ 45 $45 y$
50-60 3 55 165
60-70 1 65 65
Total $17 + x + y$ $605 + 15 x + 45 y$
2 marks
The sum of frequencies is 25:
$17 + x + y = 25 \Rightarrow x + y = 8 ...(i)$
½ mark
Mean $= \frac{\sum f _{i} x _{i}}{\sum f _{i}}$ :
$35 = \frac{605 + 15 x + 45 y}{25}$
½ mark
$605 + 15 x + 45 y = 875 \Rightarrow 15 x + 45 y = 270 \Rightarrow x + 3 y = 18 ...(ii)$
1 mark
Subtract (i) from (ii): $2 y = 10$ , so $y = 5$ .
Then $x = 8 - 5 = 3$ .
** $x = 3$ , $y = 5$ **
1 mark

Class	$f_{i}$	$x_{i}$	$f_{i} x_{i}$
0-10	1	5	5
10-20	$x$	15	$15 x$
20-30	5	25	125
30-40	7	35	245
40-50	$y$	45	$45 y$
50-60	3	55	165
60-70	1	65	65
Total	$17 + x + y$		$605 + 15 x + 45 y$

Answer: $x = 3$ , $y = 5$

Where the marks are

Correct table of class marks and $f_{i} x_{i}$ (2 marks)
$x + y = 8$ from the total frequency (½ mark)
Sets up the mean equation (½ mark)
Simplifies to $x + 3 y = 18$ (1 mark)
Solves to get $x = 3$ and $y = 5$ (½ + ½ marks)

Revise the chapter

Chapter: Statistics (notes, formulas, where marks are lost and every past question)
Topic: Mean of Grouped Data: Direct Method

Practise this chapterBoard-style questions from Statistics, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/1/1 (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 35

Hints

Step-by-step solution

Revise the chapter

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