Question

A town is supplied with water from a big overhead tank which is fed with a constant volume of water regularly. When the tank is full, if 32000 gallons are used daily, the supply fails in 50 days. However, if 37000 gallons are used daily, the supply lasts for 40 days only. How much water can be used daily without the supply ever failing?

• A. 20000 gallons
• B. 18000 gallons
• C. 15000 gallons
• D. 12000 gallons
• E. 32000 gallons

Hint:

This is a classic "inflow and outflow" problem. The difference in total water used over different time periods gives the total inflow over the difference in days, allowing you to solve for the daily inflow rate.

Answer 1

The Correct Option is D

Step 1: Define Variables:
Let the tank's full capacity be $C$ gallons. Let the constant volume of water fed into the tank per day be $F$ gallons.
Step 2: Form Equations:
In the first scenario: Usage = 32000 gal/day. Supply lasts 50 days. Total water used = $50 \times 32000 = 16,00,000$ gallons. This water comes from the initial full tank ($C$) plus the inflow over 50 days ($50F$). So, $C + 50F = 16,00,000$. (1) In the second scenario: Usage = 37000 gal/day. Supply lasts 40 days. Total water used = $40 \times 37000 = 14,80,000$ gallons. So, $C + 40F = 14,80,000$. (2)
Step 3: Solve the System:
Subtract (2) from (1): $(C+50(f) - (C+40(f) = 16,00,000 - 14,80,000$. $10F = 1,20,000 \implies F = 12,000$ gallons/day.
Step 4: Interpret:
$F$ is the rate at which the tank is refilled. If daily usage equals the inflow rate, the tank will never be depleted. Thus, the safe daily usage is 12,000 gallons.
Step 5: Final Answer:
12000 gallons can be used daily without supply failing.