Question

The income of A and B are in the ratio 4:3 and their expenditure are in the ratio 5:4.Find the ratio of their savings if A spends three fourth of his income

Options are:
a)1:1
b)4:3
c)3:1
d)5:3​

Answer 1

$\textbf{Given:}$

$\text{A and B's income ratio=4:3}$

$\text{A and B's expendiure ratio=5:4}$

$\textbf{To find:}$

$\text{Ratio of their savings}$

$\textbf{Solution:}$

$\text{A's income=4x}$

$\text{B's income=3x}$

$\text{A's expenditure=5y}$

$\text{B's expenditure=4y}$

$\text{But}$

$\textbf{A's expenditure}\bf=\dfrac{3}{4}\;\text{of his income}$

$\implies\,5y=\dfrac{3}{4}{\times}4x$

$\implies\,5y=3x$

$\implies\,y=\dfrac{3}{5}x$

$\text{Now}$

$\text{A's savings=A's income-A's expenditure}$

$\text{A's savings}=4x-5y$

$\text{A's savings}=4x-5(\dfrac{3x}{5})$

$\text{A's savings}=4x-3x$

$\text{A's savings}=x$

$\text{B's savings=B's income-B's expenditure}$

$\text{B's savings}=3x-4y$

$\text{B's savings}=3x-4(\dfrac{3x}{5})$

$\text{B's savings}=\dfrac{15x-12x}{5}$

$\text{B's savings}=\dfrac{3x}{5}$

$\text{Ratio of their savings}$

$=x:\dfrac{3x}{5}$

$=5x:3x$

$=5:3$

$\textbf{Answer:}$

$\textbf{Option (d) is correct}$

Answer 2

Answer:

option d

Step-by-step explanation:

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