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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-16-CT
Ratio and Proportion — Full Chapter Test
Chapter: Ratio and Proportion
Topic: Complete chapter — all topics
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • This is a full-length test covering the whole chapter — every topic is included.
  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
If $a:b::b:c$, then:
  • A.$b^2=ac$
  • B.$b=ac$
  • C.$a^2=bc$
  • D.$c=ab$
2.
In direct variation, $y=$
  • A.$\tfrac{k}{x}$
  • B.$kx$
  • C.$k+x$
  • D.$x^2$
3.
In inverse variation, $xy=$
  • A.$0$
  • B.$k$
  • C.$x+y$
  • D.$x-y$
4.
$b$ is the mean proportional of $a,c$ if:
  • A.$b=a+c$
  • B.$b^2=ac$
  • C.$b=ac$
  • D.$2b=ac$
5.
If $y\propto x$ and $x$ doubles, $y$:
  • A.halves
  • B.doubles
  • C.is unchanged
  • D.squares
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the mean proportional between $4$ and $16$.
7.
If $y\propto x$ and $y=10$ when $x=2$, find $k$.
8.
If $xy=24$ and $x=6$, find $y$.
9.
Find the third proportional to $4$ and $8$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the mean proportional between $9$ and $25$.
11.
$y$ varies directly as $x$; $y=15$ when $x=5$. Find $y$ when $x=8$.
12.
$x$ varies inversely as $y$; $x=4$ when $y=6$. Find $x$ when $y=8$.
13.
Find the third proportional to $9$ and $12$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
The mean proportional between two numbers is $12$ and their third proportional is $96$. Find the numbers.
15.
If work done varies directly with the number of men, how many men are needed to do $3$ times the work in the same time as $12$ men?

Answer Key

Section A — Multiple Choice Questions
  1. (A) $b^2=ac$
  2. (B) $kx$
  3. (B) $k$
  4. (B) $b^2=ac$
  5. (B) doubles
Section B — Short Answer (2 marks)
  1. $8$.
  2. $5$.
  3. $4$.
  4. $16$.
Section C — Short Answer (3 marks)
  1. $15$.
  2. $24$.
  3. $3$.
  4. $16$.
Section D — Long Answer (5 marks)
  1. $6$ and $24$.
  2. $36$ men.
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