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A earns Rs. 80 per hour and work for 8 h...

A earns Rs. 80 per hour and work for 8 hours a day. B. earns Rs. 60 per hour and works for 6 hours a day. What is the ratio of per day wages of a and B?

A

`9:10`

B

`16:5`

C

`5:16`

D

`16:9`

Text Solution

AI Generated Solution

The correct Answer is:
To find the ratio of the per day wages of A and B, we can follow these steps: ### Step 1: Calculate A's daily earnings A earns Rs. 80 per hour and works for 8 hours a day. \[ \text{A's daily earnings} = \text{Hourly rate} \times \text{Hours worked} \] \[ \text{A's daily earnings} = 80 \times 8 = 640 \text{ Rs.} \] ### Step 2: Calculate B's daily earnings B earns Rs. 60 per hour and works for 6 hours a day. \[ \text{B's daily earnings} = \text{Hourly rate} \times \text{Hours worked} \] \[ \text{B's daily earnings} = 60 \times 6 = 360 \text{ Rs.} \] ### Step 3: Find the ratio of A's earnings to B's earnings Now, we need to find the ratio of A's daily earnings to B's daily earnings. \[ \text{Ratio of A to B} = \frac{\text{A's daily earnings}}{\text{B's daily earnings}} = \frac{640}{360} \] ### Step 4: Simplify the ratio To simplify the ratio, we can divide both the numerator and the denominator by their greatest common divisor (GCD). First, we can cancel the zeroes: \[ \frac{640}{360} = \frac{64}{36} \] Now, we can simplify further by dividing both by 4: \[ \frac{64 \div 4}{36 \div 4} = \frac{16}{9} \] ### Final Answer Thus, the ratio of the per day wages of A to B is: \[ \text{Ratio of A to B} = 16:9 \] ---
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