Question

Three friends Alice, Bond and Charlie divide Rs.1105 among them in such a way that if Rs 10, Rs 20 and Rs 15 are removed from the sums that Alice, Bond and Charlie received respectively, then the share of the sums that they got will be in the ratio of 11:18:24. How much did Charlie receive?
A. Rs 495
B. Rs 500
C. Rs 425
D. Rs 450

Answer 1

Hint: We first assume that the sum of money received by Alice, Bond and Charlie will be x, y and z respectively. So according to given condition we can write that \[x-10:y-20:z-15=11a:18a:24a\]., so, taking this equation in consideration we can write that \[11a+18a+24a=1105-(10+20+15)=1060\] so from here we get value of a equals to 20
So \[z-15=24a\] , putting the value of \[a=20\] we get a sum of money received by z which is 495.

Complete step by step answer:
Given three friends Alice, Bond and Charlie now each one gets money of x,y and z respectively now it is given that after subtracting Rs 10, Rs 20 and Rs 15 respectively from their money its ratio becomes 11:18:24, and the total sum of money is 1105. To find amount of money Charlie receive, means we have to find value of z
So, considering above conditions we can say that \[x+y+z=1105\] because sum is given as 1105
Now we write other condition in mathematical form as \[x-10:y-20:z-15=11a:18a:24a\]
So, we can equate the sum both side and write as \[x+y+z-10-20-15=11a+18a+24a\]
Which simplifies to \[x+y+z-45=53a\] , but we know that \[x+y+z=1105\]
Putting sum of x,y,z we get equation as \[1105-45=53a\], on solving we get \[1060=53a\]
So, on solving getting value an equal to \[a=20\].
Now using this \[x-10:y-20:z-15=11a:18a:24a\] we know that \[z-15=24a\]
On putting value of \[a=20\] we get equation as \[z-15=24\times 20\] which on solving resolves to
 \[z=495\]

Hence, sum of money received by z is 495.

Note: Most of the students after calculating the value of a can do the mistake by just multiplying a with 24 and tick the option \[11a:18a:24a\] but we have to read the question carefully and add
15 also \[z=24\times 20+15=495\]