# Mathematics Questions and Answers – Applications of Linear Equation (Create and Solve the Equations)

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This set of Mathematics Online Test for Class 8 focuses 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

Explanation: 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

Explanation: 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

Explanation: 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

Explanation: 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

Explanation: 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

Explanation: If a set is formed consisting all the multiples of 12 it would be like [12,24,36,48,60,…..] The set of multiples of 12 is formed by multiplying the set of natural numbers with 12.
Let the set of natural number be represented by x
∴ the general equation of multiples of 12 = 12x

7. Sita wants to buy books of five hundred-rupees and she has 12 fifty-rupees notes. How many notes will she have after the payment?
a) 1
b) 2
c) 3
d) 4

Explanation: If Sita wants to pay five hundred-rupees in fifty-rupees notes then she has to give the shopkeeper 10 notes each of fifty-rupees. After giving 10 notes, she will be left with 2 notes. Hence, the correct answer to this question is 2.

8. If Ram’s present age is 3 years and Shyam is twice Ram’s present age. What will be Shyam’s age after 10 years?
a) 16
b) 17
c) 18
d) 19

Explanation: Let Ram’s present age be x years.
∴ Shyam’s present age will be 2x years.
After 10 years Shyam’s age would be, (2x + 10) years.
∴ Shyam’s age after 10 years = 2 * 3 + 10
∴ Shyam’s age after 10 years = 6 + 10
∴ Shyam’s age after 10 years = 16 years.

9. If the perimeter of a regular hexagon is 192 m then find the Length of each side of the regular hexagon.
a) 32 cm
b) 32 m
c) 23 m
d) 23 cm

Explanation: Perimeter of a regular hexagon = 6 * (side)
∴ 192 = 6 * (side)
∴ side = 32 m.

10. If the perimeter of a scalene triangle is 23 cm, with side 1 with Length 12 cm and side 2 with Length 3 cm. Find the Length of third side.
a) 23 cm
b) 12 cm
c) 2 cm
d) 8 cm

Explanation: Perimeter of a scalene triangle = Length of side 1 + Length of side 2 + Length of side 3
∴ 23 = 12 + 3 + Length of side 3
∴ 23 = 15 + Length of side 3
∴ Length of side 3 = 8 cm.

Sanfoundry Global Education & Learning Series – Mathematics – Class 8.

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