Maths Question

1. Vicky is 5 years older than Teddy. Four years later, Teddy's age will be 3/4 of Vicky's. How old are they now?

Let the present age of Vicky be x, the present age of Teddy be y
x - y = 5...........................(1)
(x + 4)(3/4) = y + 4............(2)

From (1),
4x - 4y = 20.......................(3)
From (2),
( 3x + 12 )/4 = y + 4
3x + 12 = 4y + 16
3x - 4y = 4........................(4)

(3) - (4),
4x - 4y - 3x + 4y = 20 - 4
4x - 3x = 16
x = 16 //

Substitute x = 16 into (1)
16 - y = 5
y = 11 //

The present age of Vicky is 16, the present age of Teddy is 11

2. The denominator of a fraction is greater than the numerator by 7. If we add 5 to both of them, the fraction will be reduced to 1/2. Find the fraction.

Let the numerator be x, the denominator be y, the fraction be (x/y)
y - x = 7..............................(1)
(x+5) / ( y+5) = 1/2................(2)

From (2)
2( x+5 ) = y + 5
2x + 10 = y + 5
2x - y = -5
y - 2x = 5...............................(3)

(1) - (3),
y - x - y + 2x = 7 - 5
-x + 2x = 2
x = 2 //

Substitute x = 2 into (1)
y - 2 = 7
y = 9 //

The fraction is 2/9

1.
Vicky is 5 years older than Teddy. Four years later, Teddy's age will be 3/4 of

Vicky's. How old are they now?


Let Vicky be x years old,Teddy is y years old

x - 5 = y

4x - 20 = 4y----[1]

3(x + 4)/4 = y + 4

3x + 12 = 4y + 16------[2]

[1] - [2]

x - 32 = - 16

x = 16

y = 11



2.
The denominator of a fraction is greater than the numerator by 7. If we add 5 to both of

them, the fraction will be reduced to 1/2. Find the fraction.


let x be the denominator , y be numerator

x - 7 = y-----[1]

y + 5 / x + 5 = 1/2

2y + 10 = x + 5

x - 5 = 2y-----[2]

[2] - [1]

2 = y

x =

So,the fraction is 2/9.