Pair of Linear Equations in Two Variables Test - 12

Let my age and son's age be x and y years.
Given, x = 3y
x + 5 = 5(y + 5)/2

⇒ 3y + 5 = 5(y + 5)/2 = (5y + 25)/2
⇒ 6y + 10 = 5y + 25
⇒ y = 15
x = 3 × 15 = 45
Hence, my age and son's age are 45 years and 15 years.

Let unit digit = x , Tens digit = y , therefore original no will be 10y+x.

Sum of digits are 9 So that x + y = 9 ………….(1)

nine times this number is twice the number obtained by reversing the order of the digits 9 (10 y + x ) = 2 (10 x + y )

90y + 9x = 20 x + 2y

88y – 11x = 0    

Divide by 11 we get 8y - x = 0 …………..(2)

Adding equations 1 and 2 , we get

9 y = 9

Y = 9/9 = 1

Putting this value in equation 1 we get

x+ y = 9

x + 1 = 9

x = 8.

Therefore the number is 10(1)+8 = 18

Let the original No is 10x + y

The sum of the digits of a two digit no. Is 9. 
If the digits are reversed, 
the new no. Is 27 less than the given no. 
x + y = 9 
(10x + y) = (10y + x) - 27 
9x - 9y = -27 
x - y = -3 
x = 3
y = 6 
Then the number Is 36

Let the width be x.
then length be x+4
According to the question,
l+b=36
x+(x+4)=36
2x+4=36
2x=36-4
2x=32
x=16.
Hence, The length of the garden will be 20 m and width will be 16 m.
Area = length × breath= 20 × 16 =  320 m²

let the numbers be x and y, then as per question

x + y = 35............(1)
x - y = 13.......... (2)

Adding equation (1) & (2)
2x = 48
x = 24

Substitute this value in eq (1) we get
24 + y = 35
y = 11
Therefore the Numbers are 24 and 11