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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-16-INV-01
Inverse Variation — Assignment
Chapter: Ratio and Proportion
Topic: Inverse Variation
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • 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.
In inverse variation, $xy=$
  • A.$0$
  • B.$k$
  • C.$x+y$
  • D.$x-y$
2.
If $x\propto\tfrac1y$ and $x$ doubles, $y$:
  • A.doubles
  • B.halves
  • C.unchanged
  • D.squares
3.
If $xy=12$ and $x=3$, then $y=$
  • A.$4$
  • B.$36$
  • C.$9$
  • D.$15$
4.
"More workers, less time" is:
  • A.direct
  • B.inverse
  • C.none
  • D.joint
5.
In inverse variation, the product $xy$ is:
  • A.increasing
  • B.constant
  • C.zero
  • D.negative
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
If $xy=24$ and $x=6$, find $y$.
7.
If $x\propto\tfrac1y$ and $x=2$ when $y=5$, find $k$.
8.
If $y=\tfrac{k}{x}$ and $y=4$ at $x=3$, find $k$.
9.
If $6$ workers take $4$ days, find the total work in worker-days.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
$x$ varies inversely as $y$; $x=4$ when $y=6$. Find $x$ when $y=8$.
11.
If $8$ pipes fill a tank in $6$ hours, how long would $12$ pipes take?
12.
$15$ men finish a job in $20$ days. How many days for $25$ men?
13.
If $y\propto\tfrac1x$ and $(x,y)=(2,9)$, find $y$ at $x=3$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
$30$ workers finish a project in $24$ days. How many workers are needed to finish it in $18$ days?
15.
A car covers a fixed distance in $5$ hours at $60$ km/h. Find the time at $75$ km/h.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $k$
  2. (B) halves
  3. (A) $4$
  4. (B) inverse
  5. (B) constant
Section B — Short Answer (2 marks)
  1. $4$.
  2. $10$.
  3. $12$.
  4. $24$.
Section C — Short Answer (3 marks)
  1. $3$.
  2. $4$ hours.
  3. $12$ days.
  4. $6$.
Section D — Long Answer (5 marks)
  1. $40$ workers.
  2. $4$ hours.
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