Welcome to R&H academy
channel. Question nine of
exercise 4.3 says.
According to question,
two water taps,
fill a tank in 75 by eight
hours.
The larger tap
takes
10 less than the smaller tap
so let smaller tap;
larger tap will take
x minus
10 hours
We need to find the time in
which each tap can separately
fill the tank. So follow with me
that time taken by smaller tap
to fill one tank is x hours.
Time taken by larger tap to fill
one tank is (x-10)hrs. Larger
tap, portion of tank filled in
one hour by larger tap is
one by x minus 10.
Suppose, this is a large tap, it
takes x minus 10 hours
to fill this tank
to find out the portion of tank
filled in one hour
by the tap will be
one by x minus 10
unitary method, the portion of
tank filled in 75 by eight hour
will be one by x minus 10
multiply 75 by eight.
Now let it be a smaller tap,
we know, it takes x hours to
fill this one tank. Now how much
tank will be filled in one hour
that is one by x. In x hours,
one tank is filled. In one hour,
one by x tank will be filled and
in 75 by eight hours, one by x
multiply 75 by 8 portion of tank
will be filled by this smaller
tap. Try to understand, a small
tank takes x hours to fill one
tank. How much tank will be
filled in 1 hour, 1 by x portion
of tank. How much tank will be
filled in 75 by 8 hour.
I hope you understand the
equations now, according to
question smaller and larger tap
together fill this tank in 75 by
eight hours. So what will be our
equation. Now according to
question, larger tap plus
smaller tap together fill this
one tank in 75 by eight hours,
portion of tank
filled by larger tap
in 75 by eight ho
one by x minus 10 multiply 75 by
eight
plus
one by x multiply 75 by 8
equal to one
Now simplify it, five by eight
multiply x minus 10. 75 by eight
x equal to 1. 75 by eight is in
both
terms, take it out
remaining is by x minus 10 plus
one by x is equal to one,
Now, transpose 75 by eight to
rightside, one by x minus 10
plus one by x is equals to eight
by 75. Let's take the LCM of x
minus 10 and x. LCM of x and x
minus 10 is x multiply x minus
10. So, one by x minus 10
multiplied by multiplied and
divided by x.
Similarly,
mult iply and divide one by x b
 x minus 10 equal to x multiply 
 minus 10 plus x minus 10 divide
 by x multiply x minus 10 i
 equal to eight by 75 X plus 
 minus 10 divided by x multiply 
 minus 10 equal to eight by 75
 Now, simplify it further, x plu
 x is two x minus 10 is equal t
eight by 75. Now, cross multiply
75 multiply two x is 150 x. 75
multiply 10 is 750. 8x multiply
x is eight x square and eight x
multiply ten is eighty x.
Transpose these terms to the
left side. Now rearrange the
terms minus eight x square
plus 150 x
plus 80 x minus 750 is equal to
zero, divide the entire equation
by minus two, this is an
optional step minus two divided
by zero is zero. use the
quadratic formula Or spreading
the middle term or completing
the square method to find the
value of x, my favorite is
quadratic formula
A is four B is minus 115 and C
is 375. d is equal to b square
minus 4ac
minus multiply minus hundred 14
square
minus four, multiply four,
multiply 375. 115 Square is
hundred 15 Square is 13,225 and
four multiply four multiply 375
is
6000
and 13,235 minus 6000 is 7225.
So x is equals to minus p plus
minus root d by two a, now,
substitute the values minus 115
plus minus 7225 divided by two,
multiply four. x is equals to
plus hundred 15 plus minus 7225
square root divided by eight. To
find the square root of 7225,
find out its prime factor, and
you'll get 85 divided by eight.
x is equal to hundred and 15
plus 85 by eight and x is equal
115 minus eight five by eight.
115 plus 85 is 200 by eight,
which is equal to 25 and  115
minus 85 is 30 by eight or 15 by
four, Remember, x is time taken
by a smaller tap to fill the
tank. So, case one when x is 15
by four
or
x is equals to 3.75.
So x minus 10 will be
3.75 minus 10. Now, x minus 10
is time taken by larger tap
375 minus 10 is
minus 6.25 Can time or hour be
negative? Nope. So x won't be
15/4
Now let's see case two, when x
is 25. So, x minus 10 will be 25
minus 10. That is 15.
Hence, smaller tap
takes
25 hours to fill the tank
and larger tap
takes 15 hours
to fill the tank.
I hope this problem is clear to
you. It's bit interesting and
tricky. So, I recommend you do
watch the video again. And if
you have any doubts, let me know
in the comment section and do
not forget to subscribe the
channel and share the video with
your friends. Thank you
