In the year 2001, a man spends 40% of his total income on food.

Question

In the year 2001, a man spends 40% of his total income on food. In 2002 his income increases by 40% and his expenditure on food increases by 50% with respect to 2001. In 2003 his income increases by another 25% based on 2002 and his expenditure on food increase by 16.66% based on the expenditure on food in 2001. What percent of his total income in 2003 is his expenditure on food ?

A. 66.67%
B. 50%
C. 37.5%
D. 33.33%
E. 26.67%

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hr1212 · Answer

Year 
 Income 
 Food expense 
 
  2001 
 100 
 40 
 
  2002 
 100 * 1.4 = 140 
 40 * 1.5 = 60 
 
  2003 
 140 * 5/4 = 175 
 40 * 7/6 = 140/3

Food percentage =  \frac{(140/3) * 100}{175} = \frac{140 * 4}{3 * 7} = \frac{80}{3} = 26.67

IMO: E

eega · Answer

Year 
 Income 
 Expenditure 
 
  2001 
 100 
 40 
 
  2002 
 100x1.4 = 140 
 40x1.5 = 60 
 
  2003 
 140x1.25= 175 
 40x7/6 = 140/3

Food percentage = ((140/3)/175)x100 = 26.67

Option E

Whoisdmx15 · Answer

Assume, 
in 2001 Total Income = 100, Food = 40
in 2002 Total Income = 100*1.4 = 140 Food = 40*1.5 = 60
In 2003 Total Income = 140*5/4= 175 Food = 40*(1+1/6) = 140/3

Hence required percentage: (140/3)/175*100 = 26.67%

IMO Ans E

bhargavhhhhhhhh · Answer

Step 1: Define Variables
Let the income in 2001 be I.
- Food expenditure in 2001 = 40% of I = 0.4I.

Step 2: Calculate for 2002
- Income increase: 40% increase → New income in 2002
 I_2002 = I + 0.4I = 1.4I
- Food expenditure increase: 50% increase over 2001 → New food expenditure in 2002
 F_2002 = 0.4I + (0.5 × 0.4I) = 0.4I + 0.2I = 0.6I

Step 3: Calculate for 2003
- Income increase: 25% increase over 2002
 I_2003 = 1.4I + 0.25(1.4I) = 1.4I × 1.25 = 1.75I
- Food expenditure increase: 16.66% increase over 2001 food expenditure
 F_2003 = 0.4I + (0.1666 × 0.4I) = 0.4I + 0.0666I = 0.4666I

Step 4: Find Percentage of Income Spent on Food in 2003
 (F_2003 / I_2003) × 100 = (0.4666I / 1.75I) × 100

Cancel I:
 = (0.4666 / 1.75) × 100
 ≈ 26.67%

Final Answer:
E. 26.67%

In the year 2001, a man spends 40% of his total income on food.

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Year	Income	Food expense
2001	100	40
2002	100 * 1.4 = 140	40 * 1.5 = 60
2003	140 * 5/4 = 175	40 * 7/6 = 140/3

Year	Income	Expenditure
2001	100	40
2002	100x1.4 = 140	40x1.5 = 60
2003	140x1.25= 175	40x7/6 = 140/3

GMAT Problem Solving (PS) Questions

In the year 2001, a man spends 40% of his total income on food.

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