Question

The ratio of expenditure and savings is 3 : 2. If the income increase by 15% and the savings increases by 6%, then by how much percent should his expenditure increases ?

• A. 25
• B. 21
• C. 12
• D. 24

Answer 1

The correct option is B 21

$\frac{expenditure}{saving}=\frac{3}{2}=k$ (let)

$\frac{expenditure}{saving}=\frac{3k}{2k}$

Income$=3k$

Saving$=2k$

Income$=3k+2k$

$=5k$

$\therefore$ Income increased $=5k+\frac{15\times 5k}{100}$

$=5k+\frac{15\times 5k}{100}$

$=\frac{20k+3k}{4}$

$=\frac{23k}{4}$

Saving increase by $6$

$\therefore$ New saving $=2k+\frac{6\times 2k}{100}$

$=2k+\frac{3k}{25}$

$=\frac{53k}{25}$

New Expenditure$=(\frac{23k}{4}-\frac{53k}{25})$

$=\frac{363k}{100}$

Now,

Increase in expenditure $=\frac{363k}{100}-3k$

$=\frac{363k-3k}{100}$

$=\frac{63k}{100}$

$\therefore$ Percent increase in expenditure$=\frac{63k}{100\times 3k}\times 100\%$

$=21\%$