Pair of Linear Equation in Two Variables Test

Result

Pair of Linear Equation in Two Variables Test - 1

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

The sum of the digits of a two-digit number is 6. Also, twice of this number is 6 more than the number obtained by reversing the order of the digits. Find the number.

A
21

B
23

C
24

D
25

Solution

Let the unit digit and tens digit of the number be x and y respectively.
Then, the number = 10y + x
Number after reversing the digits = 10x + y
According to the given information, x + y = 6 ..........(i)
2 ( 10y + x ) = 6 + ( 10x + y )
⇒ 20y + 2x = 6 + 10x + y
⇒ 20y - y + 2x - 10x = 6
⇒ 19y - 8x = 6 ..........(ii)

From, eq (i), we get
x = 6 - y
Now putting this in eq (ii), we get
19y - 8 ( 6 - y ) = 6
⇒ 19y - 48 + 8y = 6
⇒ 27y = 6 + 48
⇒ 27y = 54
⇒ y = 2

Thus, substituting it back in eq (i)
x + 2 = 6
x = 6 - 2
x = 4
Thus, the required number is 10y + x = 10 (2) + 4 = 20 + 4 = 24
Question 2
1 / -0

Arya starts his job with certain monthly salary and earns a certain increment every year. If his salary was Rs. 6,300 after 6 years of service and Rs. 7,200 after 12 years, find his initial salary and annual increment respectively.

A
5400, 150

B
5300, 200

C
5200, 150

D
5100, 200

Solution

Let the annual increment be Rs. y. And initial salary be Rs. x.
According to the question, x + 6y = 6300 ...............(i)And x + 12y = 7200 ...........(ii)
Subtracting (ii) from (i) we have x + 6y - x + 12 y = 6300 - 7200 -6y = - 900
6y = 900
y = 900 ÷ 6
= 150

Putting the value of y in (i) we have x + 6y = 6300
x + 6 (150) = 6300
x + 900 = 6300
x = 6300 - 900
x = 5400