Question

Example 3: Sum of salaries of A and B. salaries of B and C and that
of A and Care in the ratio of 4:5:7 respectively.If sum of salaries
of A Band C is Rs. 48120, what is the salary of A?​

Answer 1

$\huge{\underline{\purple{\rm{Solution:}}}}$

$\large{\underline{\red{\rm{Let:}}}}$

• $\rm{The\:sum\:of\: ratio\:of\: their\: salaries\:be\:x}$

• $\rm{The\: Salary\:(A+B)=4x}$

• $\rm{The\: Salary\:(B+C)=5x}$

• $\rm{The\: Salary\:(A+C)=7x}$

$\large{\underline{\red{\rm{Given:}}}}$

• $\rm{The\:sum\:of\: salary\:of(A+B+C)=48120}$

$\large{\underline{\red{\rm{To\: Find:}}}}$

• $\rm{The\: salary\:of\:A}$

$\small{\underline{\purple{\rm{According\:to\: above\: information:}}}}$

$\rm{\implies (A+B)+(B+C)+(A+C)=4x+5x+7x}$

$\rm{\implies 4x+5x+7x=2A+2B+2C}$

$\rm{\implies 16x=2(A+B+C)}$

$\rm{\implies \cancel{16}x=2*\cancel{48120}}$

$\rm{\implies x=2*3007.5}$

$\rm\purple{\implies x=6015}$

• $\rm{Putting\:the\:value\:of\:x=6015}$

$\rm{The\: Salary\:(A+B)=4*6015}$

$\rm\red{(A+B)=24060----(i)}$

$\rm{The\: Salary\:(B+C)=5*6015}$

$\rm\green{(B+C)=30075----(ii)}$

$\rm{The\: Salary\:(A+C)=7*6015}$

$\rm\purple{(A+C)=42105----(iii)}$

• $\rm{Now,\: solving\:eq\:i\:and\:ii}$

$\rm{\implies A+B=24060}$

$\rm{\implies B+C=30075}$

• $\rm{by\: solving\:we\:get\: here,}$

$\rm\orange{\implies A-C=-6015----(iv)}$

• $\rm{Now,\: solving\:eq\:iii\:and\:iv}$

$\rm{\implies A+C=42105}$

$\rm{\implies A-C=-6015}$

• $\rm{by\: solving\:we\:get\: here,}$

$\rm{\implies \cancel{2}A=\cancel{36090}}$

$\rm{\implies A=18045}$

Hence,

$\rm\purple{The\: salary\:of\:A=Rs.18045}$

Answer 2

Let the salaries of A, B and C be $\sf{a,\ b}$ and $\sf{c}$ respectively.

Given that sum of salaries of A, B and C is Rs.48120.

$\longrightarrow\sf{a+b+c=48120\quad\quad\dots(1)}$

Given that sum of salaries of A and B, B and C, and C and A are in the ratio of 4 : 5 : 7, i.e.,

$\longrightarrow\sf{(a+b):(b+c):(c+a)=4:5:7}$

So let,

• $\sf{a+b=4x\quad\quad\dots(2)}$

• $\sf{b+c=5x\quad\quad\dots(3)}$

• $\sf{c+a=7x\quad\quad\dots(4)}$

On adding (2), (3) and (4),

$\longrightarrow\sf{(a+b)+(b+c)+(c+a)=4x+5x+7x}$

$\longrightarrow\sf{2(a+b+c)=16x}$

From (1),

$\longrightarrow\sf{2\times48120=16x}$

$\longrightarrow\sf{x=6015}$

Then (3) becomes,

$\longrightarrow\sf{b+c=5\times6015}$

$\longrightarrow\sf{b+c=30075\quad\quad\dots(5)}$

On subtracting (5) from (1),

$\longrightarrow\sf{(a+b+c)-(b+c)=48120-30075}$

$\longrightarrow\sf{\underline{\underline{a=18045}}}$

Hence the salary of A is $\bf{Rs.\,18045.}$