Question

Two water tanks at PPV Aman and PPV Damai consists of x and 3000 litres of water, respectively, on the first day.

a) Subsequently, y litres of water is used from the tank in PPV Aman everyday. Volume of water left at the end of 18th day is 2520 litres and the tank will be expected empty by the day 81. Find the value of x and y. [8 marks]

b) The usage of water in PPV Damai constantly 30 litres per day. Find the day for both, tank at PPV Aman and PPV Damai, has the same amount of water. [4 marks]

Answer 1

From the question, we have that:

PPV Aman has $x$ litres

PPV Damai has $3000$ litres

(a) since the PPV Aman tank contains $x$ litres.

$y$ litres of water is used daily and on the 18th day, the tank remains $2520$ litres

Gives the equation

$x-18y=2520$ --------------------------- equ(i)

Also,The tank is expected empty on the 81st day implies

$x-81y=0$ --------------------------------equ(ii)

Bringing both equations together and Solving both equ(i) and equ(ii) simultaneously

$x-18y=2520$ ---------------equ(i)

$x-81y=0$ --------------------------------equ(ii)

Making $x$ the subject of equations in both equ(i) and equ(ii)

$x=2520+18y$ ------------------equ(iii)

$x=81y$ --------------------------------equ(iv)

Equating equ(iii) and equ(iv)

$2520+18y=81y$

$2520=81y-18y$

$2520=63y$

Dividing both sides by 63

$y= \frac{2520}{63}$

$y=40$

Substitute $y=40$ in equ(iv)

$x=81y$

$x=81(40)$

$x=3240 litres$

(b) To get the numbers of days for both thanks to have the same left over of water.

$3240=2*2*2*3*3*3*3*5$

$3000=2*2*2*3*5*5*5$

The H.C.F =$2*2*2*3*5=120$

It then follows that

$\frac{3240}{120}+\frac{3000}{120}$

$25+27=52$

At the $52nd$ day, the two tanks will equal to each other.