Mira's expenditure and savings are in the ratio $3 : 2$ . Her income increases by $10$ $%$ . Her expenditure also increases by $12$ $%$ . By how much $%$ do her savings increases?

7

%

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9

%

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10

%

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13

%

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Solution

The correct option is D $7$ $%$
Let Mira's expenditure and savings be $3 x$ and $2 x$ respectively.
Then her income $= 5 x$
Increased income $= \frac{110}{100} \times 5 x = 5.5 x$
Increased expenditure $= \frac{112}{100} \times 3 x = 3.36 x$
$∴$ Increased savings $=$ $5.5 x - 3.36 x = 2.14 x$
$∴$ $%$ increase in savings $= (\frac{2.14 x - 2 x}{2 x} \times 100) % = (\frac{0.14 x}{2 x} \times 100) % = 7 %$

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Mira's expenditure and savings are in the ratio 3:2. Her income increases by 10 %. Her expenditure also increases by 12 %. By how much % do her savings increases?

The correct option is D 7 %Let Mira's expenditure and savings be 3x and 2x respectively. Then her income =5xIncreased income =110100×5x=5.5xIncreased expenditure =112100×3x=3.36x∴ Increased savings = 5.5x−3.36x=2.14x∴ % increase in savings =(2.14x−2x2x×100)%=(0.14x2x×100)%=7%

Mira's expenditure and savings are in the ratio $3 : 2$ . Her income increases by $10$ $%$ . Her expenditure also increases by $12$ $%$ . By how much $%$ do her savings increases?