Question

The ratio of income of A and B is 3: 2 and the ratio of their expenditure is 4: 3 and their savings are respectively 2000 and 1000 find the income of A and B respectively.
A.3000, 4000
B.4000, 6000
C.5000, 6000
D.6000, 4000

Answer 1

Hint: Suppose the income of A and B in terms of x and expenditure of A and B in terms of y, then form the equation and solve it.

Complete step-by-step answer:
The ratio of incomes of A and B is 3 : 2
Let the incomes of A and B are 3x and 2x.
The ratio of expenses of A and B is 4: 3 or, Expenses of A and B are 4y and 3y
We know that, saving = Income – expenses.
Saving of A = 3x – 4y = 2000 ––––––––I
Saving of B = 2x – 3y = 1000 ––––––––II
On solving these two equations, we get
3x – 4y = 2000 ––––––––I
2x – 3y = 1000 ––––––––II
Multiply equation 1 by 2 and equation II by 3
$\begin{array}{l}
6x - 8y = 4000\\
\dfrac{{6x - 8y = 3000}}{{y = 1000----\;\left( {III} \right)}}
\end{array}$
Put this value in eqn. 1 we get
3x – 4y = 2000
⇒ 3x – 4 × 1000 = 2000
⇒ 3x = 2000 + 4000
⇒ $x = \dfrac{{6000}}{3}$
x = 2000
Therefore, Income of A = 3x = 3 × 2000 = 6000
Income of B = 2x = 2 × 2000 = 4000
So, from the above option only the D option is correct.

Note: It is recommended that write all the equations carefully in terms of x and y and don’t leave only after finding the value of x Find complete share of A and B, if you are supposing something like A = 3x & B = 2x put value and get final answer.