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Simultaneous Linear Equations MATHEMATICS - Simultaneous Linear Equations

ICSE - STD 9 - MATHEMATICS (ICSE - English Medium). 199 questions in this chapter.

Question types

Simultaneous Linear Equations question types

199 questions across 4 question groups — pick any mix to generate a MATHEMATICS paper with step-by-step answer keys.

199
Questions
4
Question groups
5
Question types
Sample Questions

Simultaneous Linear Equations questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1[3 marks sum]3 Marks
If three times the larger of the two numbers is divided by the smaller, then the quotient is 4 and remainder is 5. If 6 times the smaller is divided by the larger, the quotient is 4 and the remainder is 2. Find the numbers.
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Q 2[3 marks sum]3 Marks
If from twice the greater of the two numbers, 45 is subtracted, the result is the other number. If from twice the smaller number, 21 is subtracted, the result is the greater number. Find the numbers.
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Q 3[3 marks sum]3 Marks
Find two numbers such that the sum of twice the first and thrice the second is 103 and four times the first exceeds seven times the second by 11.
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Q 4[3 marks sum]3 Marks
A and B together can do a piece of work in 6 days. If A's one day's work be $1 \frac{1}{2}$ times the one day's work of B, find in how many days, each alone can finish the work.
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Q 6[4 marks sum]4 Marks
A man travels 600 km partly by train and partly by car. If he covers 120 km by train and the rest by car, it takes him 8 hours. But, if he travels 200 km by train and the rest by car, he takes 20 minutes longer. Find the speed of the car and that of the train.
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Q 7[4 marks sum]4 Marks
If 11 pens and 19 pencils together cost ₹ 502; while 19 pens and 11 pencils together cost ₹ 758, how much 3 pens and 6 pencils cost together?
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Q 8[4 marks sum]4 Marks
The sum of the digits of a two-digit number is 12. If the digits are reversed, the new number is 12 less than twice the original number. Find the original number.
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Q 9[4 marks sum]4 Marks
Find the fraction which becomes $\frac{1}{2}$ when its numerator is increased by 6 and is equal to $\frac{1}{3}$ when its denominator is increased by 7 .
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Q 11[5 marks sum]5 Marks
If 2 is added to each of the two given numbers, then their ratio becomes 1 : 2. However, if 4 is subtracted from each of the given numbers, the ratio becomes 5 : 11. Find the numbers.
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Q 12[5 marks sum]5 Marks
Of the two numbers, 4 times the smaller one is less than 3 times the larger one by 6. Also, the sum of the numbers is larger than 6 times their difference by 5. Find the numbers.
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Q 14[5 marks sum]5 Marks
A motorboat takes 6 hours to cover 100 km downstream and 30 km upstream. If the motorboat goes 75 km downstream and returns back to its starting point in 8 hours, find the speed of the motorboat in still water and the rate of the stream.
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Q 15[5 marks sum]5 Marks
The area of a rectangle gets reduced by 8 m2, if its length is reduced by 5 m and breadth increased by 3 m. If we increase the length by 3 m and breadth by 2 m, the area is increased by 74 m2. Find the length and breadth of the rectangle.
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Q 16MCQ1 Mark
If $8 x+9 y=42 x y$ and $2 x+3 y=12 x y$, then the value of $\frac{1}{x y}$ is :
  • A
    1
  • B
    4
  • ✓
    6
  • D
    $\frac{1}{6}$

Answer: C.

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Q 17MCQ1 Mark
If $a x-b y=a^2+b^2$ and $\frac{x+y}{2}=a$, then the value of $x-y$ is :
  • A
    a
  • B
    2a
  • C
    b
  • ✓
    2b

Answer: D.

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Q 18MCQ1 Mark
If $0.4 x+0.3 y=2.3$ and $2.5 x-2 y=-5$, then the value of $x y$ is :
  • ✓
    10
  • B
    12
  • C
    2.4
  • D
    1.2

Answer: A.

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Q 19MCQ1 Mark
Assertion (A) : A pair of linear equations in two variables cannot have more than one solution.
Reason (R) : If we solve a pair of linear equations in two variables, first by elemination method and then by cross multiplication method, then in some cases the two solutions so obtained may be different.
  • ✓
    A is true, R is false
  • B
    A is false, R is true
  • C
    Both A and R are true
  • D
    Both A and R are false.

Answer: A.

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Q 20MCQ1 Mark
Assertion (A) : $\frac{2}{m}+\frac{3}{m}=0$ and $\frac{2}{3 m}+\frac{2}{n}=\frac{1}{6}$ is a pair of simultaneous linear equations.
Reason (R) : An equation of the form $a x+b y+c=0, a \neq 0, b \neq 0$ is called a linear equation in two variables.
  • A
    A is true, R is false
  • ✓
    A is false, R is true
  • C
    Both A and R are true
  • D
    Both A and R are false.

Answer: B.

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