[CLASS 8] Mathematics MCQs on Applications of Linear Equation (Create and Solve the Equations)

Mathematics Online Test for Class 8 on “Applications of Linear Equation (Create and Solve the Equations)”.

1. The digits of a two-digit number differ by 4. If the digits are interchanged, and the resulting number is added to the original number, we get 152. What can be the original number?
a) 95
b) 40
c) 73
d) 59
Answer: a
Clarification: Let us take the two digit number such that the digit in the units place is x. The digit in tens place differs by 4 ∴ the digit in tens place is (x + 4).
∴the two digit number obtained = [10 * (x + 4)] + [x]
∴the two digit number obtained = 10x + 40 + x
∴the two digit number obtained = 11x + 40
When the digits are interchanged we obtain the number = [10 * x] + [(x + 4)]
The new number obtained = 11x + 4
As we know the original number and the new number add up to 152.
∴ [11x + 40] + [11x + 4] = 152
∴ 22x + 44 = 152
∴ 22x = 110
∴ x = 5
The original number = [10 * ( x + 4 )] + [x]
The original number = 11x + 40
The original number = 11 * (5) + 40
The original number = 55 + 40
The original number = 95.

2. Jon is thrice as old as Kavya. Five years ago his age was two times Kavya’s age. Find their present age.
a) Kavya’s age = 15 years; Jon’s age = 5 years
b) Kavya’s age = 5 years; Jon’s age = 15 years
c) Kavya’s age = 5 years; Jon’s age = 5 years
d) Kavya’s age = 15 years; Jon’s age = 15 years
Answer: b
Clarification: Let us consider Kavya’s age as x years.
Then Jon’s age would be 3x years.
Kavya’s age five years ago was (x – 5) years.
Jon’s age five years ago was (3x – 5) years.
It is given that Jon’s age five years ago was two times Kavya’s age.
Thus, (3x – 5) = 2 * (x – 5)
Or 3x -5 = 2x – 10
Or x = 5
∴ Jon’s age = 3x
∴ Jon’s age = 3 * 5
∴ Jon’s age = 15 years
∴ Kavya’s age = x
∴ Kavya’s age = 5 years.

3. Arya takes a number adds (frac{13}{3}) to it and then divides it by 3. At the end of all operations he gets 12. What would be the original number?
a) (frac{23}{3})
b) (frac{3}{23})
c) 23
d) 3
Answer: a
Clarification: Let the number chosen by Arya be x.
The first operation carried out by Arya was adding (frac{13}{3}) to the number.
Hence, the equation formed is x + (frac{13}{3}) = 12
The second operation is to divide throughout by 3.
Hence, the equation is modified to (frac{x}{3} + frac{13}{9}) = 4
(frac{x}{3} + frac{13}{9}) = 4
∴ (frac{3x}{9} + frac{13}{9} = frac{36}{9})
∴ 3x + 13 = 36
∴ 3x = 23
∴ x = (frac{23}{3}).

4. When a number is subtracted from 484, we get 459. The number subtracted is square of?
a) 5
b) 4
c) 3
d) 2
Answer: a
Clarification: Let the number subtracted be x.
484 – x = 459
∴ 484 – 459 = x
∴ x = 25
∴ the subtracted number is 25 and 25 is square of number 5.

5. Raj buys books worth rupees four hundred, he has coins of denomination two-rupees. How many coins does he need to pay the bill?
a) 200
b) 100
c) 400
d) 150
Answer: a
Clarification: Let the number of coins required be x.
The amount to be paid is rupees 400.
(2 * x) = 400
∴ 2x = 400
∴ x = 200
Raj needs 200 coins each of two rupees in order to pay the bill amount.

6. Form an equation for all multiples of 12.
a) 3x
b) 12x
c) 4x
d) 3x