On one day a rickshaw puller earned Rs. `160`. Out of his earnings he spent Rs. `26(3)/(5)` on tea and snacks, Rs. `50(1)/(2)` on food and Rs. `16(2)/(5)` on repairs of the rickshaw. How much did he save on that day?

Options

A. `Rs. 66(1)/(2) `
B. `Rs. 76(1)/(2) `
C. `Rs. 88(1)/(2) `
D. `Rs. 69(1)/(2) `

Answer

To find out how much the rickshaw puller saved on that day, we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
1. **Tea and Snacks:**
- The amount spent is Rs. \(26 \frac{3}{5}\).
- Convert to improper fraction:
\[ 26 \frac{3}{5} = \frac{(26 \times 5) + 3}{5} = \frac{130 + 3}{5} = \frac{133}{5} \]

2. **Food:**
- The amount spent is Rs. \(50 \frac{1}{2}\).
- Convert to improper fraction:
\[ 50 \frac{1}{2} = \frac{(50 \times 2) + 1}{2} = \frac{100 + 1}{2} = \frac{101}{2} \]

3. **Repairs of Rickshaw:**
- The amount spent is Rs. \(16 \frac{2}{5}\).
- Convert to improper fraction:
\[ 16 \frac{2}{5} = \frac{(16 \times 5) + 2}{5} = \frac{80 + 2}{5} = \frac{82}{5} \]

### Step 2: Find a Common Denominator
To add these fractions, we need a common denominator. The denominators are 5 and 2. The least common multiple (LCM) of 5 and 2 is 10.

### Step 3: Convert Each Fraction to Have a Common Denominator
1. **Tea and Snacks:**
\[ \frac{133}{5} = \frac{133 \times 2}{5 \times 2} = \frac{266}{10} \]

2. **Food:**
\[ \frac{101}{2} = \frac{101 \times 5}{2 \times 5} = \frac{505}{10} \]

3. **Repairs of Rickshaw:**
\[ \frac{82}{5} = \frac{82 \times 2}{5 \times 2} = \frac{164}{10} \]

### Step 4: Add the Expenses
Now we can add all the expenses:
\[ \text{Total Expenses} = \frac{266}{10} + \frac{505}{10} + \frac{164}{10} = \frac{266 + 505 + 164}{10} = \frac{935}{10} \]

### Step 5: Calculate Savings
The rickshaw puller earned Rs. 160. To find out how much he saved, we subtract the total expenses from his earnings:
\[ \text{Savings} = 160 - \frac{935}{10} \]

Convert Rs. 160 to a fraction with a denominator of 10:
\[ 160 = \frac{1600}{10} \]

Now, subtract:
\[ \text{Savings} = \frac{1600}{10} - \frac{935}{10} = \frac{1600 - 935}{10} = \frac{665}{10} \]

### Step 6: Convert to Mixed Number
Convert \(\frac{665}{10}\) to a mixed number:
\[ \frac{665}{10} = 66 \frac{5}{10} = 66 \frac{1}{2} \]

### Final Answer
The rickshaw puller saved Rs. \(66 \frac{1}{2}\).

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