A boat's upstream speed is 60 kmph and downstream speed is 80 kmph. Find its still water speed and the current speed.
Show answer Hide answer
Answer: A. 70, 10 kmph
Explanation
Still water speed is calculated by taking one-half of the sum of the downstream and upstream speeds. Adding eighty and sixty gives one hundred forty, and dividing by two yields a still water speed of seventy kilometers per hour. Current speed is calculated by taking one-half of the difference between downstream and upstream speeds, yielding ten kilometers per hour. Upstream speed equals the boat velocity in still water minus the speed of the river current. Downstream speed equals the boat velocity in still water plus the speed of the river current. Averaging opposing velocities allows mathematicians to isolate individual speed components from relative motion data.
Option B suggests speeds of thirty-five and twenty-seven, which fail to yield the given downstream and upstream totals. Option C proposes fifty and sixty, creating incorrect sums and differences when compared to the problem statement. Option D offers forty-five and fifty-five, which do not match the mathematical averages of eighty and sixty.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. A worker's wage is increased by 30% and subsequently cut by 30%. What is the net percentage change?
Show answer Hide answer
Answer: C. 9% decrease
Successive percentage changes of equal magnitude in opposite directions always yield a net decrease. Squaring the percentage value of thirty and dividing by one hundred gives nine percent. The net result of a thirty perc...
Q2. A commodity tax drops by 20% while consumption rises by 15%. What is the net impact on revenue_________?
Show answer Hide answer
Answer: B. It decreases by 8%
Revenue is calculated as the product of the commodity tax rate and total consumer consumption. Applying sequential percentage changes using the net change formula accounts for both opposing factors. Combining a twenty pe...
Q3. Three numbers sum to 98. The first-to-second ratio is 2:3 and the second-to-third is 5:8. Find the second number:__________?
Show answer Hide answer
Answer: B. 30
Combining two sequential ratios into a single continuous ratio yields ten to fifteen to twenty-four. Summing the parts of the combined ratio gives a total of forty-nine proportional parts overall. Multiplying the fractio...
Q4. The true discount on a bill due in 9 months at 16% per annum is Rs. 189. Find the total bill amount:
Show answer Hide answer
Answer: B. Rs. 1764
Substituting the true discount, interest rate, and time period into the discount formula yields the principal. Solving the equation for the total bill amount incorporates the nine month duration at sixteen percent. The e...
Q5. Haroon's motorcycle tank of petrol lasts 10 days. If he starts using 25% more fuel daily, how many days will a full tank last?
Show answer Hide answer
Answer: D. 8days
An increase in daily fuel consumption by twenty five percent raises the daily usage rate proportionally. Dividing the original tank capacity duration by the new consumption multiplier determines the remaining days. Calcu...
Q6. A two-digit number has a tens digit two greater than its units digit, and equals 7 times the sum of its digits. Find the units digit.
Show answer Hide answer
Answer: B. 2
Expressing the two-digit number algebraically using tens and units variables sets up a linear equation. Substituting the condition that the tens digit exceeds the units digit by two into the equation. Solving the resulti...