Equations in One Variable Test

Result

Equations in One Variable Test - 4

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Weekly Quiz Competition

Question 1
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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 2
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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

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 3
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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 = 21/3 = 7

Numbers are 7 and 35.