Equations in One Variable Test

Result

Equations in One Variable Test - 9

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Question 1
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Rajan got married eight years ago. His present age is 6/5 times his age at the time of his marriage. Rajan's sister was 10 years younger to him at the time of his marriage. The present age of Rajan's sister is

A
32 years

B
36 years

C
38 years

D
40 years

Solution

Let Rajan's present age be x years.
Then, his age at the time of marriage = (x - 8) years
Therefore, x = 5x = 6x - 48
x = 48
Rajan's sister's age at the time of his marriage = (x - 8) - 10 = (x - 18) = 30
Rajan's sister's present age = (30 + 8) = 38 years
Question 2
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Find the value of 'x' after simplifying the equation = ^.

A

B

C

D

Solution

=
=
=
=
=
65x + 15 = 72x + 144
65x – 72x = 144 – 15
– 7x = 129
x =
Question 3
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What will be the value of 'x' in the linear equation - 0.4x + 0.17x = 1.24?

A
- 3.31

B
- 6.24

C
3.76

D
6.76

Solution
Question 4
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Find the value of 'x'.

x - = + 1

A
0

B
1

C
2

D
3

Solution

x - = + 1

x - =

x - =
=
=

2(-7x + 1) = 3(3x - 7)

-14x + 2 = 9x - 21

-14x - 9x = -21 - 2

-23x = -23

Hence, x = 1
Question 5
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What is the value of 'x' in the equation ?

A
-10

B
0

C
10

D

Solution

(3x - ) = 1
= 1
= 1
= 1

6(2x - 1) = 14(1 + x)
12x - 6 = 14 + 14x
14x - 12x = -14 - 6
2x = -20
Hence, x = -10
Question 6
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The sum of the digits of a 2-digit number is 12. If 36 is added to the number, its digits get interchanged. What is the number?

A
34

B
57

C
48

D
84

Solution

Let the digit at unit's place be x.
So, the digit at ten's place = 12 – x
Number = 10 (12 – x) + x
= 120 – 10 x + x
= 120 – 9x
The number with its digit interchanged =
10x + (12 – x) = 9x + 12
(120 – 9x) + 36 = 9x + 12
156 – 12 = 18x
144 = 18x
x = 8
Number at unit's place = 8
Number at ten's place = 4
Hence, the required number is 48.
Question 7
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A company manufactures 1500 pairs of gloves, 2500 pieces of caps and certain pairs of socks. Each pair of gloves costs $30, each cap costs $40 and each pair of socks costs $35. If the total cost for all the items is $179195, then what will be the number of pairs of socks manufactured?

A
977

B
850

C
1040

D
1260

E
1310

Solution

Suppose, X pairs of socks are manufactured.
According to question,
30 1500 + 40 2500 + 35X = 179195
45000 + 100000 + 35X = 179195
35X = 179195 - 145000
X = 34195 ÷ 35= 977
Number of pairs of socks manufactured = 977
Question 8
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What will be the value of 'z' in the equation – + = ?

A

B

C

D

E

Solution

- + = – + – = 0
= 0
210z – 945 – 245z – 280 + 90z + 60 – 21z – 168 = 0
= (210 – 245 + 90 – 21)z = 945 + 280 – 60 + 168
34z = 1333
z =
Question 9
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A positive number is 5 times the other number. If 21 is added to both the numbers, then greater of the two numbers becomes twice the smaller number. What are the numbers?

A
5 and 25

B
7 and 35

C
6 and 30

D
8 and 40

Solution

Let one number be x.
Other number = 5x
Adding 21 to both numbers, they become x + 21 and 5x + 21, respectively.
According to the question, we have
5x + 21 = 2(x + 21) (As 5x + 21 is greater)
5x + 21 = 2x + 42
5x - 2x = 42 - 21
3x = 21
x = = 7
Numbers are 7 and 35.
Question 10
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Vivek has Rs. 40 in the form of 25 paisa coins and 50 paisa coins. If the number of 25 paisa coins is twice the number of 50 paisa coins, how many coins of each kind (50 paisa and 25 paisa, respectively) does he have?

A
45 and 90

B
40 and 80

C
50 and 100

D
35 and 70

Solution

Let the number of 50 paisa coins be x and the number of 25 paisa coins be 2x.
Total money = Rs.40
Therefore,

Number of 50 paisa coins = 40
Number of 25 paisa coins = 40 2 = 80
Question 11
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What will we get on dividing 100 into two parts in such a way that of one part is equal to of the other?

A
20, 80

B
30, 70

C
40, 60

D
50, 50

Solution

Let one part be x.

Other part = 100 - x

According to the question,

(x) = (100 - x)
8x = 200 - 2x
8x + 2x = 200
10x = 200
x = 20
One part = 20
Other part = 100 - 20 = 80
Question 12
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Three consecutive integers, when taken in increasing order and multiplied by 2, 3 and 4, respectively, add up to 83. What are these numbers?

A
7, 8 and 9

B
8, 9 and 10

C
9, 10 and 11

D
10, 11 and 12

Solution

Let three consecutive integers be x, x + 1 and x + 2.
According to the question,
2x + 3(x + 1) + 4(x + 2) = 83
i.e. 2x + 3x + 3 + 4x + 8 = 83
i.e. 9x + 11 = 83
9x = 72
x = = 8
Three consecutive integers = 8, 9 and 10
Question 13
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Which of the following is true for the equation 13(y – 4) – 3(y – 9) – 5(y + 4) = 0?

A
y = 4

B
y = 9

C
y = 5

D
y = 13

Solution

13(y - 4) - 3(y - 9) - 5(y + 4) = 0
13y - 52 - 3y + 27 - 5y - 20 = 0

5y - 45 = 0 y = = 9
y = 9
Hence, (2) is the correct option.
Question 14
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A shop owner had a certain amount of sugar. He sold of the sugar plus 1 kg to the 1^st party, of the remaining sugar to the 2^nd party and of the remaining sugar plus 1 kg to the third party. At last, he was left with 130 kg of sugar. What was the quantity of sugar that the shop owner had initially?

A
384 kg

B
438 kg

C
273 kg

D
504 kg

E
612 kg

Solution

Let the total amount of sugar be x kg.
Then, x - = (x - 1) kg of sugar is left after the 1^stsale.
So, - = (x - ) kg of sugar is left after the 2^nd sale.
Finally, (x - ) - 1 kg of sugar is left after the final sale.
So, x - - x + - 1 = 130
= 130 + + 1 -
= 131 + -
=
= x = ×
x = 438 kg
Question 15
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If 6 + = , what is the value of x?

A

B

C

D

E
None of these

Solution

6 + = = 6 +
=
1 + = = 1 +
=
1 + = = 1 +
x = 4/3