Pooja spends 10% of her monthly income on rent, 20% of the remaining on food, and 50% of the remaining on traveling. If the difference between the amount she spends on traveling and that on rent is Rs. 52000, then find the monthly income (in Rs.) of Pooja.

A. Rs. 70000
B. Rs. 150000
C. Rs. 2000
D. Rs. 5000
E. Rs. 200000

Pooja's monthly income is Rs. 200,000. This is calculated based on her expenditures on rent, food, and traveling, and the difference in amounts spent on traveling and rent is Rs. 52,000. The mathematical representation showed that her income is derived from the equation involving her percentages of spending.
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Answered by Anonymous | 2025-07-04

To solve this problem, we need to determine Pooja's monthly income based on the percentages she spends and the given difference between her spending on traveling and rent.
Let's denote Pooja's monthly income as x .

Rent:


Pooja spends 10% of her monthly income on rent, which is 0.10 x .


Remaining after Rent:


After spending on rent, Pooja is left with 90% of her income, which is 0.90 x .


Food:


She spends 20% of the remaining amount on food. Thus, on food, she spends: 0.20 × 0.90 x = 0.18 x

Remaining after food: 0.90 x − 0.18 x = 0.72 x



Traveling:


She spends 50% of the remaining amount, after food, on traveling. Therefore, on traveling, she spends: 0.50 × 0.72 x = 0.36 x


Difference between Traveling and Rent:


According to the problem, the difference between the amount she spends on traveling and rent is Rs. 52000: 0.36 x − 0.10 x = 52000 0.26 x = 52000


Solving for Monthly Income x :


To find x , divide Rs. 52000 by 0.26: x = 0.26 52000 ​ x = 200000

Thus, Pooja's monthly income is Rs. 200,000.
The correct option is (E) Rs. 200,000.

Answered by danjohnbrain | 2025-07-06