58. In the summer, water consumption is known to decrease overall by 25%. A water Board official
states that in the summer household consumption decreases by 20%, while other consumption
increases by 70%
Which of the following statements in correct?
(a) The ratio of household to other consumption is 8/17
(b) The ratio of household to other consumption is 1/17
(c) The ratio of household to other consumption is 17/8
(d) There are errors in the official’s statement.
Problem: In summer, total water consumption decreases by 25%. Water Board official claims household consumption drops 20% while other consumption increases 70%. Which ratio is correct or are there errors?
Mathematical Setup
Let initial other consumption = O
Total initial consumption = T = H + O
Summer total (↓25%) = 0.75T
Official claims:
Household (↓20%) = 0.8H
Other (↑70%) = 1.7O
Consistency equation: 0.8H + 1.7O = 0.75(H + O)
Solving the Equation
1.7O – 0.75O = 0.75H – 0.8H
0.95O = -0.05H
H = -19O
Conclusion: Negative household consumption is impossible!
Option Analysis
(a) Ratio H:O = 8/17
H = 8k, O = 17k
Summer: 0.8(8k) + 1.7(17k) = 6.4k + 28.9k = 35.3k
Expected: 0.75(25k) = 18.75k
35.3k > 18.75k → Inconsistent
(b) Ratio H:O = 1/17
H = k, O = 17k
Summer: 0.8k + 1.7(17k) = 0.8k + 28.9k = 29.7k
Expected: 0.75(18k) = 13.5k
Still increases → Wrong
(c) Ratio H:O = 17/8
H = 17k, O = 8k
Summer: 0.8(17k) + 1.7(8k) = 13.6k + 13.6k = 27.2k
Expected: 0.75(25k) = 18.75k
Increases → Incorrect
✅ (d) Errors in official’s statement
Final Answer: The equation yields impossible negative household consumption. Official’s claims cannot both be true with 25% overall decrease.
Key Takeaway
The mathematical inconsistency proves the official’s statement contains errors. This classic GATE aptitude question tests logical reasoning through quantitative analysis.
