Problem Set 1 : Bankers Discount - Quantitative Aptitude Video Lecture | Quantitative for GMAT

the true discount on able of rupees 540
is 90 rupees
what is the bankers discount so the
bankers discount is nothing but the
simple interest on the amount which is
rupees 540 right this is the amount okay
now we have been given that the true
discount on a bill of 540 is 90 rupees
so the amount is given and the true
discount of that amount is 90 degrees
right but what is true discount well
true discount is actually the simple
interest on the principal worth right on
the present worth of the money and
that's 90 now how do you calculate the
present worth well amount is actually it
is equals to the principal amount plus
the true discount right true discount is
basically the interest on the principal
amount so amount is 540 and we have P
which is we want to calculate plus true
discount is 90 so the present worth of
the money is 540 minus 90 and that is
450 right so principal is 450 now we can
write this as you know true discount is
the simple interest on the present worth
and true discount is 90 so I can write
90 is equals to the simple interest on
the present worth that is rupees 450
right so we have two proportions we can
cross multiply and equate so we want to
calculate the bankers discount so I have
the bankers discount is equal to 90
times 540 divided by 450 right so this
is equal to when calculated this gives
you 108 so the bankers discount is 108
rupees the present
of a certain bill do some time hence is
rupees 800 and the true discount is 36
rupees
what is the bankers discount so we have
been given the true discount that is 36
so true discount is basically equals to
the simple interest on the principal
worth that is the present worth and that
is given to us as 800 so 36 is the
simple interest on 800 rupees right I
can write this now we have been asked
what is the bankers discount so bankers
discount is basically the simple
interest on the amount but we don't have
the amount right so how do we calculate
amount now 36 is the simple interest on
800 right so principle is equals to 800
and interest is basically 36 right so we
can calculate the amount amount is
basically principal plus interest so
amount will be equals to 800 plus 36 and
that's 836 isn't it so I can write the
bankers discount is equals to the simple
interest on the amount that is 836 right
so just cross-multiply any quit and you
can get the value of VD that is the bank
of discount so the bankers discount is
equals to 800 and 36 times 36 divided by
800 right and that will give you 30 7.62
so our answer is option B 30 7.62 rupees
which is the bank wills discount the
bankers gain of a certain sum due to
years hence at 10% per annum is 24
rupees what is the present worth okay so
what is the formula for calculating the
bankers gain well bankers gain is equal
to the bankers discount minus the true
discount right this is in standard
formula we have been given the bankers
gain and that is 24 rupees so I can
write 24 is equals to what is the
formula for calculating the bankers
discount
well bankers discount is calculated on
the amount it is basically the simple
interest on the
right so let the amount be a so I can
write a times n times R n s 2 so this is
two times rate of interest is 10 so 10
upon 100 right p NR upon 100 so similar
to that - true discount is basically the
interest calculated on the present worth
right so let the present worth be P so
this is equals to P times n R upon 100 n
is 2 times R is 10 upon 100 right so
this gets cancelled out 2 times 5 is 10
here also 2 times 5 is 10 this 0 already
cancels out so 24 is equals to I have a
minus P divided by 5 isn't it so 24
times 5 is 122 a minus P now what is a
minus P amount minus the present worth
or amount minus the principal it is
actually the interest and this interest
which is calculated on the principal is
the true discount so I can say true
discount is equal to 120 right but what
do we need we need the present worth so
what is the formula for calculating the
true discount well true discount is
equals to P n R upon hundred is that
correct so true discount is 120 so I can
write 120 is equals to P times 2 times
10 upon hundred and these zeroes get
cancelled out 2 times 60 is 120 so I
have the present worth as 60 times 10
that is 600 rupees right so option C is
the correct answer
the bankers discount on a bill do 4
months hence at 15% is 420 rupees what
is the true discount so the bankers
discount is actually the simple interest
calculated on the amount for the
unexpired time so I can write it as a n
R upon 100 right a times n what is n
well n is 4 months to write it in years
I need to write it as 4
12 years then times rate rate is 15% on
hundred right now 4 times 3 is 12
so I have 3 times 5 as 15 that bankers
discount is given to us as 420 this is
equals to amount which is a times 5 upon
hundred right so PI times 20 is 100 for
20 times 20 is 8400 which is equal to
the amount right now you have got the
amount you can calculate the true
discount true discount is equals to you
know the formula it is 8 times n times R
upon we have 100 plus n times R this is
the formula if you know the amount right
so this can be written as 8400 times n
times R well this is 4 by 12 times 15
let's cancel it here itself 4 times 3 is
12 3 times 5 is 15 divided by I have 100
plus n times R is basically 5 right this
term so 8400 times 5 that is 42,000
divided by 105 and that is equal to 400
right so true discount is 400 rupees so
option a is the correct answer