A man spends 80% of his income. If his income is increased by 40% and expenditure is increased by 10%, by what percentage is savings increased?

Question

Actual Answer is $160\%$.

What I have done: I took his income as $100$. According to the question, his income is increased by $40$ so, $140$.

According to the question, his expenditure is $80$, then his expenditure increased by $10\%$ so $90\%$.

According to the question, the man's saving is $20$ because $100-80 = 20$, After his expenditure increased by $10\%$ his new saving is $50$, i.e $140 - 90 = 50$.

I want to find the percentage of saving is increased, so from saving difference $50 - 20$ is $30$.

$30/20 \times 100 = 150\%$. I got $150\%$, but the answer is $160\%$.

Answer 1

Hint : His initial expenditure is $80$. It is increased by $10 \%$, so it becomes $\frac{110}{100}.80 = 88$ and not $90$.

So his new saving is $52$, which you can check yields the correct answer.

Answer 2

Logically, An income $I$ is sum of Expenditure/Spending $E$ and Saving $S$.

So,

$I=E+S$

Let's assume that, His income is \$100.

Then, $\text E=\$80$, and $\text S=\$20$.

Now, If income is increasing by $40%$, then

$I=I+0.40I=1.40I=1.40*100=140$

And you are also increasing E by 10, then

$E=1.10E=1.10*80=88$

So,

$S=140-88=52$.

Now, %age increase in saving

$$={\frac{(52-20)}{20}}*100=32/20*100=160$$

Answer 3

Let income be 100 Expenditure is 80 Saving is 20 New salary 140 i.e 40% of 100+100 New expenditure 80*10/100=8 i.e 80+8=88 New saving =140-88=52 Difference in saving=52-20=32 % of increase in saving =32/20*100=160%