Kerala Syllabus Class 9 Maths: Unit 01 Pairs of Equations - Questions and Answers


Questions and Answers for Class 9th Mathematics (English Medium) സമവാക്യജോ‍ടികള്‍ | Text Books Solution Mathematics (English Medium) Chapter 01 Pairs of Equations

ഒമ്പതാം ക്ലാസ്സ്‌ Maths ലെ Pairs of Equations എന്ന പാഠം ആസ്പദമാക്കി തയ്യാറാക്കിയ ചോദ്യോത്തരങ്ങള്‍ താഴെ നൽകിയിരിക്കുന്നു. 

Maths: Unit 01 Pairs of Equations
∎Samagra Mathematics Notes
1. The price of three pens and two pencils is 40 rupees. The price of three pens and 3 pencils is 45 rupees. The price of pencils is
Answer: 5 rupees

2. Three pens and three pencils cost 45 rupees. What is the cost of 5 pens and 5 pencils.       
Answer: Cost of 1 pen and 1 pencil is 45/ 3 = 15

3. 5 kg orange and 3 kg grape costs 500 rupees. 5 kg orange and 2 kg rape cost 450 rupees.The cost of 1kg grape is
Answer: 50 rupees

4. 11𝑥 + 10𝑦 = 40, 10𝑥 + 11𝑦 = 44, What is 21𝑥 + 21𝑦
Answer: 84

5. If 11𝑥 + 10𝑦 = 40, 10𝑥 + 11𝑦 = 44, then 𝑥 + 𝑦 is
Answer: 4

6. Perimeter of a rectangle is 24cm. If the sides are 𝑥 and y then 10𝑥 + 10𝑦 is
Answer: 
𝑥 + 𝑦 = 12
10𝑥 + 10𝑦 = 120

7. 𝑥 and 𝑦 are two consecutive natural numbers and 𝑥+y is 41. The sum of their successors is
Answer: 43

8. If 𝑥 + 𝑦 = 8, 2𝑥 + 𝑦 = 10, then what is 𝑥 
Answer: 2

9. 𝑥 and 𝑦 are the perpendicular sides of a right triangle. Hypotenuse is 13 and 𝑥 𝑦 = 60. The sum of the perpedicular sides 𝑥 + 𝑦 is
Answer: 17

10. This is an incompleted magic square.The sum of numbers along rows, columns and diagonals are equal. What is 𝑥 + 𝑦?
Answer: 13

11. Perimeter of a rectangle is 40cm. Length is 8 cm more than it breadth. If 𝑥 is the breadth and 𝑦 is the length then
a) Write the equations 
b) Find the sides of the rectangle.
Answer: 
𝑥 + 𝑦 = 20
𝑥 + 𝑥 + 8 = 20
𝑥 = 6, 𝑦 =14

12. Sum of two numbers is 34. The difference is 10
a) If 𝑥 and 𝑦 are the numbers then write the equations
b) Find the numbers
Answer: 
𝑥 + 𝑦 = 34
𝑥 - 𝑦 = 10
𝑥 = 22 , 𝑦 = 12

13. The sum of two numbers is 73 and their difference is 37
a) If 𝑥 and 𝑦 are the numbers then write the equations 
b) Find the numbers
Answer: 
𝑥 + 𝑦 = 73
𝑥 - 𝑦 =37
𝑥 = 55, 𝑦 = 18

14. Third of the sum of two numbers is 14, and half of the difference of these numbers is 4.
a) If 𝑥 and 𝑦 are the numbers then write the equations 
b) Find the numbers
Answer: 
𝑥 + 𝑦 = 42
𝑥 - 𝑦 = 8
𝑥 = 25, 𝑦 = 17

15. 19th of the sum of two numbers is 4 and the difference is 30
a) If 𝑥 and 𝑦 are the numbers then write the equations 
b) Find the numbers
Answer: 
𝑥 + 𝑦 = 76
𝑥 - 𝑦 = 30
𝑥 = 53, 𝑦 = 23
16. Half the sum of two numbers is 20 and three times their difference is 12.
a) If 𝑥 and 𝑦 are the numbers then write the equations 
b) Find the numbers.
Answer: 
𝑥 + 𝑦 = 40
𝑥 - 𝑦 = 4
𝑥 = 22, 𝑦 = 18

17. A, B, C, D have 290 rupees between them. A has twice as much as C.
B has three times as much as D. Also, C and D together have rupees 50 less than A.
a) Write the equations 
b) Find how much amount each has?
Answer: 
a) a + b + c + d = 290, 
a = 2c, 
b = 3d, 
c + d = a - 50
b) a=140, b=60, c=70, d=20

18. Four times Bhanu's age exeeds Arun's age by 20 years. Third of Arun's age is less than Bhanu's age by 2 years.
a) Write the equations 
b) Find their ages.
Answer: 
If Bhanu's age is 𝑥 and Arun's age is y,
4𝑥 - 𝑦 = 20
3𝑥 - 𝑦 = 6
𝑥 = 14, 𝑦 = 36

19. Sum of the perimeters of two squares is 48 cm. Side of one square is 2cm more than side of other square.
a) If x and 𝑦 are the sides  then write the equations
b) Find the side of each square
Answer: 
𝑥 + 𝑦 = 12
𝑥 - 𝑦 = 2
𝑥 = 7, 𝑦 = 5

20. A steel wire of length 20m is bent in the shape of a rectangle. One side of the rectangle is 4m longer than other side. If 𝑥 and 𝑦 are the sides then 
a) Write the equations 
b) Find the length of sides
Answer: 
𝑥 + 𝑦 = 10
𝑥 - 𝑦 = 4
𝑥 = 7, 𝑦 = 3

21. The difference between acute angles of a right triangle is 50. If 𝑥 and 𝑦 are the acute angles then 
a) What is 𝑥 + 𝑦?
b) Write the equations 
c) Find the angles.
Answer: 
𝑥 + 𝑦 = 90
𝑥 - 𝑦 = 50
𝑥 = 70, 𝑦 = 20

22. Sum of the digits of a two-digit number is 5. The digit inthe  unit place is 1 more than digit in tens' place. Let x be the digit in one's place and 𝑦 the digit in tens' place 
a) Write the equations 
b) Find the digits 
c) Write the number
Answer: 
𝑥 + 𝑦 = 5
𝑥 - 𝑦 = 1
𝑥 = 3, 𝑦 = 2

23. 𝑥 five-rupee coins and y ten-rupee coins cost 80 rupees. 𝑥 ten-rupee coins and y five-rupee coins cost 70 rupees.
a) Write the equations 
b) Find the number of coins of each denomination
Answer: 
5𝑥 + 10𝑦 = 80
10𝑥 + 5𝑦 = 70
𝑥 = 4, 𝑦 = 6

24. An object moves along a line. It starts with the speed um/s. It each second speed increases with the rate am/s². The speed after t seconds can be determined by the equation of mation v = u+at. Given that speed after 4 seconds is 40m/s. speed after 10 seconds is 64 m/s.
a) Write the equations using the given information
b) Calculate initial speed u and acceleration a
Answer: 
u + 4a = 40
u + 10a = 64
u = 24 m/s, a = 4 m/s²

25. If 𝑥 + 𝑦 = 16, 𝑦 + z = 14, 𝑥 + z =10
a) What is 𝑥 + 𝑦 + z?
b) Find 𝑥, 𝑦 and z
Answer: 
𝑥 + y + z = 20
𝑥 = 6, 𝑦 = 10, z = 4
26. 4 chairs and 3 tables cost 2100 rupees. 5 chairs and 2 tables cost 1750 rupees.
a) Write the pair of equations
b) Find the cost of chair and table.
Answer: 
4𝑥 + 3𝑦 = 2100
5𝑥 + 2𝑦 = 1750
𝑥 = 150, 𝑦 = 500

27. The sum of two numbers is 8. The sum is four times their difference. If 𝑥 and 𝑦 are the numbers and 𝑥 > 𝑦
a) Write the equations
b) Find the numbers
Answer: 
𝑥 + 𝑦 = 8
4𝑥 - 4𝑦 = 8
𝑥 = 5 , 𝑦 = 3

28. Sum of the digits of a two-digit number is 13. If the number is subtracted from the number obtained by reversing the digits, the result is 45. 
a) If x is the digit in tens place and y is the digit in ones' place, then what is the number
b) Write the equations 
c) Find the number.
Answer: 
𝑥 + 𝑦 = 13 
𝑦 - 𝑥 = 5 
number = 49

29. A rectangle is divided into three small rectangles. Some lengths and areas are written in the figure.
a) Write two equations using the data given in the figure 
b) Find x and y
c) What is the area of  the  outer rectangle 
Answer: 
4 𝑥 = 𝑦 + 1, 5 𝑥 = 3 + 𝑦 
𝑥 = 2, 𝑦 = 7

30. 𝑥 and 𝑦 are two positive integers such that 𝑥² - 𝑦² = 11
a) What is 𝑥+𝑦?
b) What is 𝑥-𝑦?
c) Find 𝑥 and 𝑦
Answer: 
𝑥 + 𝑦 = 11 
𝑥 - 𝑦 = 1 
𝑥 = 6 , 𝑦 = 5

31. A father is 3 times as old as his son. After 12 years, his age will be two times as that of his son 
a) If 𝑥 is father's present age and 𝑦 is son's present age, then write the ages after 12 years.
b) Write the equations 
c) Find the present ages.
Answer: 
𝑥 = 3𝑦 𝑥+12 = 2 (𝑦 +12) 
𝑥 = 36, 𝑦 =12

32. In a trapezium total length of the parallel sides is 20 metres. Among the parallel sides longer side is 4 metres more than other side. The distance between parallel sides is 4 metres and area 40m²
a) If 𝑥 and 𝑦 are lengths of parallel sides then write the equations 
b) Find the length of parallel sides 
Answer: 
𝑥 + 𝑦 = 20 𝑥 - 𝑦 = 4 𝑥 = 12m, 
𝑦 = 8 m 
Area = 40 sq m

33. The incomes of A and B are in the ratio 9:7. Their expenditure are in the ratio 4:3. If each saves 200 rupees.
a) Write the equations
b) Find their incomes.
Answer: 

34. In ∆ABC ∠A = 𝑥°, ∠B = (3𝑥 - 2°), ∠C = 𝑦°. Also given that ∠C - ∠B = 9°
a) Write the equations 
b) Find 𝑥
c) Write the angles.
Answer: 
𝑥 + (3𝑥 - 2) + 𝑦 = 180
𝑦 - (3𝑥 - 2) = 9
𝑥 = 25
∠A = 25°, ∠B = 73°, ∠C = 82°

35. The sum of the reciprocals of two numbers is ⁷⁄₁₂. The difference of the reciprocals is ¹⁄₁₂.
a) If x and y are the numbers write the reciprocals 
b) Write the equations 
c) Find the numbers
Answer: 
a) 1/𝑥, 1/𝑦
b) 12𝑥 + 12y = 7𝑥𝑦
    12𝑦 - 12𝑥 = 𝑥𝑦
c) 𝑥 = 3, 𝑦 = 4
36. In ∆ABC ∠A = 𝑥°, ∠B = 3𝑥°, ∠C = 𝑦° and 3𝑦 - 5x = 30°
a) Write the equations 
b) Find the angles
c) What kind of triangle is this?
Answer: 
a) 4𝑥 + 𝑦 = 180
-5𝑥 + 3𝑦 = 30
b) ∠A = 30°, ∠B = 90°, ∠C = 60°
c) This is a right-angled triangle.

37. In triangle ABC  ∠C = 3 X ∠B = 2 (∠A + ∠B). Find the angles of this triangle.
Answer: 
If ∠A = 𝑥
∠B = 2𝑥
∠C = 6𝑥
9𝑥 = 180
𝑥 = 20
∠A = 20°
∠B = 40°
∠C = 120°
38. Three equations are given below
1x+1y=6, 

1y+1z=7,

1z+1x=5

Find x,y ,z:

Hint: Add the equations. 


39. Four years ago the age of a person was thrice that of his son. Eight years later, the age of person will be twice that of his son. Find their present ages.
Answer: 
Fathers present age 𝑦, sons present age 𝑥
𝑦 - 4 = 3 (𝑥 - 4), 𝑦 + 8 = 2 (𝑥 + 8)
𝑥 = 16
𝑦 = 40

40. Solve the equations
0.4𝑥 + 0.3𝑦 = 1.7
0.7𝑥 - 0.2𝑦 = 0.8
Hint: Multiply both equations by 10
Answer: 
8𝑥 + 6𝑦 = 34, 21𝑥 - 6𝑦 = 24
𝑥 = 2, 𝑦 = 3


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