A man saves a certain portion of his income during a year

Question

A man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses. Next year his income increases by 40% but his savings increase by 100%. If his total expenditure in 2 years is double his expenditure in 1st year, What %age of his income in the first year did he save?

a.) 45%
b.) 40%
c.) 25%
d.) 28%
e.) 33.33%

Can anyone please tell it's difficulty level also

A. 45%
B. 40%
C. 25%
D. 28%
E. 33.33%

chetan2u · Accepted Answer

I year 
Best is to give a number to his income, say 100..
and let saving be x..
so expenditure = 100-x

next year- 
Income = 140
savings = 2x
expenditure = 140-2x..

Now 140-2x+100-x = 2(100-x)...
240-3x = 200-2x ................x = 40...

saving % = 40/100 * 100 = 40%
B..

Q must be around 700 level

Divyadisha · Answer

1st year Income= I
1st year savings= S
1st year Expense= E1

2nd year Income = 1.4I
2nd year savings= 2S (100% increase)
2nd Year expense= E2

Now with the given information
E1+ E2= 2E1
E2=E1

That means Expenses are same during both years. With increase of 40% income the savings increased by 100%.

or S= .4I
or S= 40% of Income

B is the answer

Abhishek009 · Answer

ALTERNATE APPROACH

Use answer options for this question -

Attachment:

Capture.PNG [ 16.62 KiB | Viewed 11841 times ]

Only option (B) satisfies the condition

If his total expenditure in 2 years is double his expenditure in 1st year

Thus answer will be option (B)

PS : Feel free to post your queries in case of any doubt , I will be more than happy to respond.. :-D

luisdicampo · Answer

Deconstructing the Question

Let the man's first-year income be   I   and his first-year savings be   S  .

Then his first-year expenditure is

I-S

Next year, his income increases by  40\% , so it becomes

1.4I

His savings increase by  100\% , so they become

2S

Thus his second-year expenditure is

1.4I-2S

The key idea is that the total expenditure in 2 years is double the expenditure in the first year.

So the second-year expenditure must be equal to the first-year expenditure.

Step-by-step

First-year expenditure

I-S

Second-year expenditure

1.4I-2S

The problem states that total expenditure in 2 years is double the first-year expenditure

(I-S)+(1.4I-2S)=2(I-S)

Simplify

2.4I-3S=2I-2S

0.4I=S

So the fraction of first-year income saved is

\frac{S}{I}=\frac{0.4I}{I}=0.4

Thus he saved

40\%

Answer B

bbedran · Answer

It is easy to solve with a system of equations.

First year, his salary is 100%, savings = S, and expenditure = E
Since his salary increased by 40%, his salary became 140%. His savings doubled, so 2S and Expenditure remained the same.

(1) S + E = 100%
(2) 2S + E = 140%

Subtract first from second, and you are left with S=40%

A man saves a certain portion of his income during a year

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A man saves a certain portion of his income during a year

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