Linear Equations in One variable Test

Result

Linear Equations in One variable Test - 1

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Question 1
1 / -0

Find the value of x in 3(7x + 2) - 4(4x - 1) = 8(3x + 4) - 4(5x - 4).

A
0

B
16

C
38

D
None of these

Solution

3(7x + 2) - 4(4x - 1) = 8(3x + 4) - 4(5x - 4)
21x + 6 - 16x + 4 = 24x + 32 - 20x + 16
21x - 16x - 24x + 20x = 32 + 16 - 6 - 4
x = 38
Question 2
1 / -0

The number 323 is divided into two parts in ratio 7 : 10. If the smaller part is increased by 5 times and bigger part is increased by 7 times, then what will be the sum of the two parts?

A
1989

B
1992

C
1995

D
1998

Solution

Let the two parts be 7x and 10x.
So, as per the information given in the question,
7x + 10x = 323
17x = 323
x = 19
Smaller part = 7x = 133
Bigger part = 10x = 190

Smaller part after increase = 133 × 5 = 665
Bigger part after increase = 190 × 7 = 1330
Required sum = 665 + 1330 = 1995
Question 3
1 / -0

A number consists of two digits whose sum is 11. If 45 is added to the original number, then its digits are interchanged. Then, the original number is

A
58

B
38

C
32

D
28

Solution

Let the digit at the units place be x.
Then, the digit at the tens place will be (11 - x).
Therefore, original number = 10(11 - x) + x
= (110 - 10x) + x
= 110 - 9x

Now, after interchanging the digits, the number formed = 10(x) + (11 - x)
= 10x + 11 - x
= 9x + 11

Now, according to the question,

110 - 9x + 45 = 9x + 11
110 + 45 - 11 = 9x + 9x
144 = 18x
x = 8

Therefore, original number is 110 - 9x.
= 110 - 72
= 38