Linear Equations in One variable Test

Result

Linear Equations in One variable Test - 4

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Question 1
1 / -0

A number consists of two digits, whose sum is 15. If 27 is added to the original number, its digits get interchanged. Find the original number.

A
87

B
78

C
69

D
96

Solution

Let the digit at the units place be x.
So, digit at the tens place = (15 - x)
Original number = 10(15 - x) + x
= 150 - 10x + x
= 150 - 9x

Now, after interchanging the digits, the number will become:
10x + 15 - x = 9x + 15

According to the question,
150 - 9x + 27 = 9x + 15
162 = 18x
x = 9

So, original number = 150 - 9x
= 150 - 9 × 9
= 150 - 81
= 69
Question 2
1 / -0

A two-digit number is more than 20 but less than 30. Twice the sum of its digits is thrice their product. What is the number?

A
23

B
21

C
27

D
24

Solution

Since the two-digit number is more than 20 but less than 30, the tens digit will be 2.
According to the question,

Let the ones digit be x.
2(2 + x) = 3(2 × x)

4 + 2x = 6x
4x = 4
x = 1

Hence, the number is 21.
Question 3
1 / -0

If the angles of a triangle are in the ratio 5 : 5 : 8, then the sum of two smaller angles is

A
50°

B
60°

C
80°

D
100°

Solution

Let the angles of the triangle be 5x, 5x and 8x.
Sum of the angles = 180°

Therefore,
5x + 5x + 8x = 180°
18x = 180°
x = 10°

So, the angles are,
5x = 50°

5x = 50°
8x = 80°

Hence, the sum of the two smaller angles is 100°.