In January 2022, Kriti paid an EMI, which was 22% of her monthly salary. She spent the remaining salary on shopping of groceries and clothes in the ratio 7 ∶ 5. She spent Rs. 18,200 on shopping of clothes. If, in February 2022, her salary increased by 16%, then what was her salary (in Rs.) in February?
64,960
Calculating Kriti's Salary and Expenditures
Let's break down the problem step by step to find Kriti's salary in February 2022.
January 2022 Salary Analysis
We are given information about Kriti's financial activities in January 2022. Let her monthly salary in January 2022 be denoted by \(S\).
- EMI Paid: 22% of her monthly salary.
- Remaining Salary: The salary left after paying the EMI.
- Shopping Expenses: The remaining salary was spent on groceries and clothes in a specific ratio.
Calculating Remaining Salary
The percentage of salary remaining after paying the EMI is:
\(100\% - 22\% = 78\%\)
So, the remaining salary is \(78\%\) of \(S\), which can be written as \(0.78S\).
Shopping Expenditure Allocation
The remaining salary (\(0.78S\)) was spent on groceries and clothes in the ratio \(7 : 5\).
The total number of ratio parts is \(7 + 5 = 12\).
- Share for groceries = 7 parts out of 12
- Share for clothes = 5 parts out of 12
The amount spent on clothes is \(\frac{5}{12}\) of the remaining salary.
Amount spent on clothes \(= \frac{5}{12} \times 0.78S\)
Finding the January Salary
We are given that Kriti spent Rs. 18,200 on shopping for clothes.
So, we can set up the equation:
\(\frac{5}{12} \times 0.78S = 18200\)
Let's simplify the fraction and decimal:
\(\frac{5}{12} \times \frac{78}{100} S = 18200\)
\(\frac{5 \times 78}{12 \times 100} S = 18200\)
\(\frac{390}{1200} S = 18200\)
Simplify the fraction \(\frac{390}{1200}\) by dividing both numerator and denominator by their greatest common divisor (30):
\(\frac{390 \div 30}{1200 \div 30} S = 18200\)
\(\frac{13}{40} S = 18200\)
Now, solve for \(S\):
\(S = \frac{18200 \times 40}{13}\)
Divide 18200 by 13:
\(18200 \div 13 = 1400\)
So, \(S = 1400 \times 40\)
\(S = 56000\)
Kriti's salary in January 2022 was Rs. 56,000.
February 2022 Salary Calculation
In February 2022, Kriti's salary increased by 16% compared to her January salary.
January Salary \( = 56000\)
Increase in salary \( = 16\%\) of 56000
Increase amount \( = 0.16 \times 56000\)
Increase amount \( = 16 \times 560\) (since \(0.16 \times 56000 = 16 \times 560\))
\(16 \times 560 = 8960\)
The increase in salary was Rs. 8,960.
Kriti's salary in February 2022 is her January salary plus the increase:
February Salary \( = \) January Salary \( + \) Increase Amount
February Salary \( = 56000 + 8960\)
February Salary \( = 64960\)
Therefore, Kriti's salary in February 2022 was Rs. 64,960.
Revision Table: Kriti's Salary Details
| Month | Salary | EMI (22%) | Remaining Salary (78%) | Shopping Ratio (Grocery:Clothes) | Clothes Spending (5/12 of remaining) |
|---|---|---|---|---|---|
| January 2022 | Rs. 56,000 | Rs. 12,320 | Rs. 43,680 | 7:5 (12 parts) | \(\frac{5}{12} \times 43680 = 5 \times 3640 = \) Rs. 18,200 (Matches given) |
| February 2022 | Rs. 64,960 (56000 + 16% increase) | N/A (Not asked) | N/A (Not asked) | N/A (Not asked) | N/A (Not asked) |
Additional Information: Understanding Percentages and Ratios in Salary Calculations
This problem involves several key mathematical concepts frequently used in personal finance and economics:
- Percentage: A percentage is a number or ratio expressed as a fraction of 100. In this problem, percentages are used to calculate EMI (\(22\%\)) and salary increase (\(16\%\)). To calculate a percentage of a value, you convert the percentage to a decimal (divide by 100) and multiply by the value. For example, \(22\%\) of \(S\) is \(0.22 \times S\).
- Ratio: A ratio is a relationship between two numbers of the same kind, usually expressed as "a to b" or \(a:b\). It shows how many times one number contains another. In this problem, the ratio \(7:5\) for grocery and clothes spending means that for every 7 units spent on groceries, 5 units are spent on clothes. The total amount spent on shopping is divided into \(7+5=12\) equal parts.
- Calculating with Ratios: If a total amount is divided in the ratio \(a:b\), the first part is \(\frac{a}{a+b}\) of the total, and the second part is \(\frac{b}{a+b}\) of the total. Here, clothes spending is \(\frac{5}{7+5} = \frac{5}{12}\) of the total remaining salary spent on shopping.
- Percentage Increase: To calculate a percentage increase, you add the increase percentage to 100%, convert to a decimal, and multiply by the original value. A 16% increase means the new value is \(100\% + 16\% = 116\%\) of the original value, or \(1.16\) times the original value. February salary \( = \) January Salary \(\times (1 + 0.16) = \) January Salary \(\times 1.16\).
These concepts are fundamental for understanding budgets, expenses, and income changes.
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