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Sagot :
To solve the problem, let's break it down step by step.
### Step 1: Determine the Total Amount of Mrs. Bfoundari's Money
Given that Mrs. Bfoundari donated [tex]\(\frac{1}{5}\)[/tex] of her money to charity and the donation amount is Rs. 180,000, we can find her total money by setting up an equation:
[tex]\[ \text{Donation to charity} = \frac{1}{5} \times \text{Total Money} \][/tex]
Given:
[tex]\[ \frac{1}{5} \times \text{Total Money} = 180,000 \][/tex]
To find the Total Money, solve for it by multiplying both sides of the equation by 5:
[tex]\[ \text{Total Money} = 180,000 \times 5 \][/tex]
[tex]\[ \text{Total Money} = 900,000 \][/tex]
So, Mrs. Bfoundari’s total money is Rs. 900,000.
### Step 2: Calculate the Amount Given to Her Son
Mrs. Bfoundari gave [tex]\(\frac{3}{10}\)[/tex] of her total money to her son. The amount given to her son can be calculated as:
[tex]\[ \text{Money Given to Son} = \frac{3}{10} \times \text{Total Money} \][/tex]
[tex]\[ \text{Money Given to Son} = \frac{3}{10} \times 900,000 \][/tex]
[tex]\[ \text{Money Given to Son} = 270,000 \][/tex]
So, she gave Rs. 270,000 to her son.
### Step 3: Calculate the Remaining Money After Charity and Son's Share
First, calculate the total fraction of the money given to charity and her son:
[tex]\[ \text{Fraction Given to Charity and Son} = \frac{1}{5} + \frac{3}{10} \][/tex]
Convert these fractions to a common denominator (10):
[tex]\[ \frac{1}{5} = \frac{2}{10} \][/tex]
[tex]\[ \frac{2}{10} + \frac{3}{10} = \frac{5}{10} = \frac{1}{2} \][/tex]
This means half of the total money has been given away to charity and her son. Therefore, the remaining amount is:
[tex]\[ \text{Remaining Money} = \text{Total Money} \times (1 - \frac{1}{2}) \][/tex]
[tex]\[ \text{Remaining Money} = 900,000 \times \frac{1}{2} \][/tex]
[tex]\[ \text{Remaining Money} = 450,000 \][/tex]
### Step 4: Calculate the Amount Given to Her Daughter
Mrs. Bfoundari gave [tex]\(\frac{1}{4}\)[/tex] of the remaining money to her daughter. The amount given to her daughter can be calculated as:
[tex]\[ \text{Money Given to Daughter} = \frac{1}{4} \times \text{Remaining Money} \][/tex]
[tex]\[ \text{Money Given to Daughter} = \frac{1}{4} \times 450,000 \][/tex]
[tex]\[ \text{Money Given to Daughter} = 112,500 \][/tex]
So, she gave Rs. 112,500 to her daughter.
### Summary
- Total Money: Rs. 900,000
- Money given to her son: Rs. 270,000
- Money given to her daughter: Rs. 112,500
### Step 1: Determine the Total Amount of Mrs. Bfoundari's Money
Given that Mrs. Bfoundari donated [tex]\(\frac{1}{5}\)[/tex] of her money to charity and the donation amount is Rs. 180,000, we can find her total money by setting up an equation:
[tex]\[ \text{Donation to charity} = \frac{1}{5} \times \text{Total Money} \][/tex]
Given:
[tex]\[ \frac{1}{5} \times \text{Total Money} = 180,000 \][/tex]
To find the Total Money, solve for it by multiplying both sides of the equation by 5:
[tex]\[ \text{Total Money} = 180,000 \times 5 \][/tex]
[tex]\[ \text{Total Money} = 900,000 \][/tex]
So, Mrs. Bfoundari’s total money is Rs. 900,000.
### Step 2: Calculate the Amount Given to Her Son
Mrs. Bfoundari gave [tex]\(\frac{3}{10}\)[/tex] of her total money to her son. The amount given to her son can be calculated as:
[tex]\[ \text{Money Given to Son} = \frac{3}{10} \times \text{Total Money} \][/tex]
[tex]\[ \text{Money Given to Son} = \frac{3}{10} \times 900,000 \][/tex]
[tex]\[ \text{Money Given to Son} = 270,000 \][/tex]
So, she gave Rs. 270,000 to her son.
### Step 3: Calculate the Remaining Money After Charity and Son's Share
First, calculate the total fraction of the money given to charity and her son:
[tex]\[ \text{Fraction Given to Charity and Son} = \frac{1}{5} + \frac{3}{10} \][/tex]
Convert these fractions to a common denominator (10):
[tex]\[ \frac{1}{5} = \frac{2}{10} \][/tex]
[tex]\[ \frac{2}{10} + \frac{3}{10} = \frac{5}{10} = \frac{1}{2} \][/tex]
This means half of the total money has been given away to charity and her son. Therefore, the remaining amount is:
[tex]\[ \text{Remaining Money} = \text{Total Money} \times (1 - \frac{1}{2}) \][/tex]
[tex]\[ \text{Remaining Money} = 900,000 \times \frac{1}{2} \][/tex]
[tex]\[ \text{Remaining Money} = 450,000 \][/tex]
### Step 4: Calculate the Amount Given to Her Daughter
Mrs. Bfoundari gave [tex]\(\frac{1}{4}\)[/tex] of the remaining money to her daughter. The amount given to her daughter can be calculated as:
[tex]\[ \text{Money Given to Daughter} = \frac{1}{4} \times \text{Remaining Money} \][/tex]
[tex]\[ \text{Money Given to Daughter} = \frac{1}{4} \times 450,000 \][/tex]
[tex]\[ \text{Money Given to Daughter} = 112,500 \][/tex]
So, she gave Rs. 112,500 to her daughter.
### Summary
- Total Money: Rs. 900,000
- Money given to her son: Rs. 270,000
- Money given to her daughter: Rs. 112,500
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