Question

Harry and Sharry together take 8 days to dig a cubical well of depth, length and width 5 metres each. If Harry is twice as fast as Sharry, then how much time would Sharry alone take to dig up a cubical well of depth, length and width 10 metres each?

• A. 216 days
• B. 192 days
• C. 144 days
• D. 208 days

Answer 1

The Correct Option is B

Calculation of Time Required for Sharry to Dig the Well 

Step 1: Calculate the Volume of the First Well

The total work required to dig the well is based on its volume. The volume of the cubical well with side 5 meters is:

\[ V = 5^3 = 125 \text{ cubic meters} \]

Step 2: Combined Rate of Work

Since Harry and Sharry together take 8 days to dig the well, the combined rate of work is:

\[ \text{Combined rate of work} = \frac{125 \text{ cubic meters}}{8 \text{ days}} = 15.625 \text{ cubic meters/day} \]

Step 3: Individual Rates of Work

Let the rate of work for Sharry be x cubic meters per day. Since Harry is twice as fast as Sharry, Harry’s rate of work is 2x cubic meters per day. Thus, the combined rate of work is:

\[ x + 2x = 15.625 \]

Simplifying:

\[ 3x = 15.625 \implies x = \frac{15.625}{3} = 5.2083 \text{ cubic meters/day} \]

Step 4: Time Taken by Sharry to Dig a Larger Well

The volume of the larger well with dimensions 10m x 10m x 10m is:

\[ V = 10^3 = 1000 \text{ cubic meters} \]

The time taken by Sharry alone to dig this well is:

\[ \text{Time} = \frac{1000}{5.2083} \approx 192 \text{ days} \]

Conclusion:

Sharry would take approximately 192 days to dig the larger well.