CBSE Class 8 Mathematics Linear Equations Assignment Set 05

Question. Solve for x: 6(3x + 2) – 5(6x – 1) = 6(x – 3) – 5(7x – 6) + 12x
(A) – 1
(B) 1
(C) 0
(D) 2
Answer : A

Question. The number 299 is divided into two parts in the ratio 5 : 8. The product of the numbers is ________.
(A) 21140
(B) 21294
(C) 21160
(D) 31294
Answer : C

Question. If (2/3)^rd of a number is 20 less than the original number, then the number is________.
(A) 60
(B) 40
(C) 80
(D) 120
Answer : A

Question. Two years ago, Mohit was three times as old as his son and two years hence, twice of Mohit’s age will be equal to five times that of his son. Then the present age of Mohit is ________.
(A) 14 years
(B) 38 years
(C) 32 years
(D) 34 years
Answer : B

Question. Sunita is twice as old as Ashima. If six years is subtracted from Ashima’s age and four years added to Sunita’s age, then Sunita will be four times that of Ashima’s age. Find the sum of their ages two years ago.
(A) 40 years
(B) 42 years
(C) 36 years
(D) 38 years
Answer : D

Question. At a party, colas, squash and fruit juice were offered to guests. One-fourth of the guests drank colas, One-third drank squash, two-fifths drank fruit juice and just three did not drink anything. How many guests were there in all?
(A) 240
(B) 180
(C) 144
(D) 190
Answer : B

Question. Which of the following statements is INCORRECT?
(A) Kusum buys some chocolates at the rate of ₹10 per chocolate. She also buys an equal number of candies at the rate of ₹ 5 per candy. She makes a 20% profit on chocolates and 8% profit on candies. At the end of the day, all chocolates and candies are sold out and her profit is ₹ 240. Therefore, Kusum buys 100 chocolates.
(B) A carpenter charged ₹ 2500 for making a bed. The cost of materials used is ₹ 1100 and the labour charges are ₹ 200/hr. So, the carpenter will work for 7 hours.
(C) On dividing ₹ 200 between A and B such that twice of A’s share is less than 3 times B’s share by 200. So, B’s share is ₹120.
(D) Madhulika thought of a number, double it and added 20 to it. On dividing the resulting number by 25, she gets 4. Hence, the required number is 45.
Answer : D

Question. Match the following.

(A) P → (iii); Q → (iv); R → (i); S → (ii)
(B) P → (iv); Q → (ii); R → (iii); S → (i)
(C) P → (ii); Q → (i); R → (iii); S → (iv)
(D) P → (iv); Q → (i); R → (ii); S → (iii)
Answer : D

Question. A steamer goes downstream and covers the distance between two ports in 5 hours while it covers the same distance upstream in 6 hours. If the speed of the stream is 1 km/hr, find the speed of the steamer in still water.
(A) 12 km/hr
(B) 11 km/hr
(C) 13 km/hr
(D) 14 km/hr
Answer : B

Question. Fill in the blanks.
(i) The solution of the equation ax + b = 0 is_______.
(ii) The shifting of a number from one side of an equation to other is _______.
(iii) If a and b are positive integers then the solution of the equation ax = b has to be always _______.
(iv) Linear equation in one variable has only one variable with power _______.

Answer : D

Question. A two digit number is less than 20. The sum of the digits is double that of their product. What is the number?
(A) 12
(B) 15
(C) 13
(D) 11
Answer : D

Question. Solve for x :
(3x+1)/16 + (2x - 3)/7 = (x + 3)/8 + (3x - 1)/14
(A) 5
(B) 10
(C) –14
(D) 12
Answer : A

Question. The perimeter of a rectangle is numerically equal to the area of rectangle. If width of rectangle is 2(3/4)cm, then its length is________.
(A) (11/3)cm
(B) (22/3)cm
(C) 11 cm
(D) 10 cm
Answer : B

Question. . A number whose seventh part exceeds its eighth part by 1, is ________.
(A) 58
(B) 56
(C) 64
(D) 68
Answer : B

Question. A number consists of two digits whose sum is 9. If 27 is subtracted from the original number, its digits are interchanged. Then the original number is ________.
(A) 53
(B) 45
(C) 92
(D) 63
Answer : D

Question. The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to its denominator, then the new number becomes 1/5. The original rational number is ______.
(A) − 5/8
(B) 5/8
(C) 3/8
(D) − 3/8
Answer : B

Question. If x - (2x - 5x - 1/3) = x-1/3 + 1/2 then, x is equal to ______.
(A) 3/2
(B) 4/7
(C) 7/3
(D) 9/2
Answer : A

Question. A number is 56 greater than the average of its third, quarter and one-twelfth. Find the number.
(A) 85
(B) 64
(C) 72
(D) 40
Answer : C

Question. If 1/3 of a number is 10 less than the original number, then the number is________.
(A) 30
(B) 15
(C) 10
(D) 27
Answer : B

Question. Find two parts of 34 such that (4/7)^th of one part is equal to (2/5)^th of the other.
(A) 16, 18
(B) 14, 20
(C) 15, 19
(D) None of these
Answer : B

Question. Which of the following statements is  CORRECT?
Statement - 1 : x = 1/2 is the solution of
(2x - 3)/4 - (2x - 1) = x - 2/3,
Statement - 2 : x = 63/2 is the solution of
2x - 17 / 2 - (x - x - 1 / 3) = 12
(A) Only Statement - 1
(B) Only Statement - 2
(C) Both Statement - 1 and Statement - 2
(D) Neither Statement - 1 nor Statement - 2
Answer : A

Question. State ‘T’ for true and ‘F’ for false.
I. An altitude of a triangle is five-third the length of its corresponding base.
If the altitude be increased by 4 cm and the base be decreased by 2 cm, the area of the triangle would remain the same. The base and the altitude of the triangle respectively is 12 cm and 20 cm.
II. The perimeter of a rectangle is 140 cm. If the length of the rectangle is increased by 2 cm and its breadth decreased by 2 cm, the area of the rectangle is increased by 66 sq. cm.
The length and breadth of the rectangle respectively is 35 cm and 30 cm.
III. The sum of two numbers is 2490.
If 6.5% of one number is equal to 8.5% of the other number, then one of the numbers will be 1411.
      I      II    III
(A) F     F    F
(B) F     T    T
(C) T     F    F
(D) T     F    T
Answer :D

Question. If the angles of a triangle are in the ratio 2 : 3 : 4, then the difference between the greatest and the smallest angle is ______.
(A) 10°
(B) 20°
(C) 30°
(D) 40°
Answer : D

Question. One-sixth of a number when subtracted from the number itself gives 25. The number is _______ .
(A) 30
(B) 32
(C) 35
(D) 28
Answer : A

Question. There were only two candidates in an election. One got 62% votes and was elected by a margin of 144 votes. The total number of voters were ________.
(A) 500
(B) 600
(C) 700
(D) 800
Answer : B
 

Short Answer Type questions
 

Question. Divide Rs 500 between A and B such that one-third share of A and half share of B are equal
Answer: Rs 300, Rs 200

Question. The price of 2 tables and 3 chairs is Rs 340 and cost of one table is Rs 20 more than the cost of one chair Find the price of each.
Answer: chair = Rs 60, Table = Rs 80

Question. A purse contains 70 coins of ten-paisa and 50-paisa. If the total value of the money is RS 19. Find the number of each type of coins.
Answer: 10 paisa coins = 40, 50 paisa coins = 30

Question. A man left one-third of his property to his son, one-fourth to his daughter and Rs 20,000 to his wife. How much money did the man leave?
Answer: Rs 48000/-

Question. one third of the length of a pole is underground, one fifth is in water and the remaining 7 metres is above water. How long is the pole?
Answer: 15 m

Question. Anil's mother is four times as old as Anil. 25 years later, she will be just twice as old as Anil will be then. Find the present age of Anil.
Answer: 10 yrs

Question. In a class of 52 students, the number of boys is \( \frac{6}{7} \) of the number of girls. How many are boys?
Answer: 24 Boys

Question. The difference between a number and two-thirds of itself is 13. Find the number.
Answer: 39

Question. A spent \( \frac{1}{2} \) of his pocket money on lunch, \( \frac{1}{3} \)rd on conveyance and gave the remaining money to B. If B got Rs 5. How much pocket money did A got ?
Answer: Rs 30

Question. The sum of three consecutive even numbers is 252. Find the numbers
Answer: 82, 84, 86