Question

In four years time,Hussain's mother will be three times as old as Hussain six years ago,his mother was seven times as old as him find.(I) Hussain present age.(ii)the age of Hussain mother when he was born​

Answer 1

Answer:

(i) 11 years old

(ii) 30 years old

Step-by-step explanation:

Let x be the current age of Hussain (in years).

Let y be the current age of Hussain's mother (in years).

Given that in four years time, Hussain's mother will be three times as old as Hussain:

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

Given that six years ago, Hussain's mother was 7 times as old as him:

$y-6 = 7(x-6)$

Solve both equations for y:

$\begin{array}{ccc}\underline{\sf Equation\;1}&&\underline{\sf Equation\;2}\\\\\begin{aligned}y+4&=3(x+4)\\y+4&=3x+12\\y&=3x+8\end{aligned}&\qquad&\begin{aligned}y-6 &= 7(x-6)\\y-6 &= 7x-42\\y &= 7x-36\end{aligned}\end{array}$

Now, set the two expressions for y equal to each other and solve for x:

$\begin{aligned}7x-36&=3x+8\\4x&=44\\x&=11\end{aligned}$

Therefore, Hussain's present age is 11 years.

Substitute x = 11 into one of the equations for y:

$\begin{aligned}y&=3(11)+8\\y&=33+8\\y&=41\end{aligned}$

Therefore, Hussain's mother is currently 41 years old.

To calculate the age of Hussain's mother when he was born, subtract Hussain's current age from his mother's current age:

$41-11=30$

Therefore, Hussain's mother was 30 years old when he was born.