Quantitative Aptitude - MCQ Practice Questions

This question tests the concept of work rate and how much work is completed in a given time period.

Step 1: Find A's work rate per day

A completes the entire work in 20 days, so the work rate is 1 part per day.

Step 2: Calculate work completed in 5 days

Multiply the daily work rate by the number of days.

Step 3: Simplify the fraction

Reduce the fraction to its simplest form by dividing both numerator and denominator by 5.

A will complete $\frac{1}{4}$ of the work in 5 days.

This question asks us to find B's daily work rate when the total job can be completed in 15 days.

Step 1: Understand work rate definition

Work rate is the fraction of total work completed per day.

Step 2: Define total work as 1 complete job

Since B completes the entire job, the total work equals 1.

Step 3: Calculate B's daily work rate

B completes the job in 15 days, so divide the work by the number of days.

B's work rate is $\frac{1}{15}$ of the job per day, which means B completes one-fifteenth of the job each day for 15 days to finish it completely.

A's rate = $\frac{1}{12}$, B's rate = $\frac{1}{18}$.

Combined rate = $\frac{1}{12}$ + $\frac{1}{18}$ = $\frac{3}{36}$ + $\frac{2}{36}$ = $\frac{5}{36}$.

Time = $\frac{36}{5}$ = 7.2 days

This question tests the concept of inverse proportionality between the number of workers and the time required to complete a fixed task.

Step 1: Calculate total work in worker-days

Work is constant regardless of the number of workers, so we multiply workers by days.

Step 2: Set up the equation with new number of workers

With 10 workers, the same 40 worker-days of work must be completed.

Step 3: Solve for the number of days

Divide total work by the number of workers to find days required.

When 10 workers work together, they will build the same wall in 4 days.

Combined rate = $\frac{1}{10}$ + $\frac{1}{15}$ + $\frac{1}{30}$ = $\frac{3}{30}$ + $\frac{2}{30}$ + $\frac{1}{30}$ = $\frac{6}{30}$ = $\frac{1}{5}$.

Time = 5 days

A completes $\frac{1}{3}$ work in 5 days, so rate = $\frac{1}{15}$ per day.

Remaining work = $\frac{2}{3}$.

Days needed = ($\frac{2}{3}$)/($\frac{1}{15}$) = ($\frac{2}{3}$) × 15 = 10 days

Combined rate = $\frac{1}{8}$, A's rate = $\frac{1}{12}$. B's rate = $\frac{1}{8}$ - $\frac{1}{12}$ = $\frac{3}{24}$ - $\frac{2}{24}$ = $\frac{1}{24}$. B takes 24 days

Let A's rate = 1/x, B's rate = 1/y.

From equations: 3/x + 2/y = $\frac{1}{4}$ and 2/x + 3/y = $\frac{1}{3}$.

Solving: x = 30 days

60% work is done in 9 days.

Rate = 0.$\frac{6}{9}$ = $\frac{1}{15}$ per day.

Total days = 1/($\frac{1}{15}$) = 15 days

When two pipes work together, their rates of filling add up. We use the concept of work rates: if a pipe fills a tank in $t$ hours, its rate is $\frac{1}{t}$ tanks per hour.

Step 1: Find the filling rate of each pipe

Pipe A fills the tank in 10 hours, so its rate is $\frac{1}{10}$ tanks/hour.

Pipe B fills the tank in 15 hours, so its rate is $\frac{1}{15}$ tanks/hour.

Step 2: Find the combined filling rate

When both pipes work together, their rates add:

Find a common denominator (LCM of 10 and 15 is 30):

Step 3: Calculate time to fill one complete tank

If the combined rate is $\frac{1}{6}$ tanks per hour, then the time to fill 1 complete tank is:

**Answer: Both pipes together will fill the tank in $6$ hours (Option B)**

A's rate = $\frac{1}{12}$, B's rate = $\frac{1}{18}$. Combined rate = $\frac{5}{36}$. In 6 hours, they fill $\frac{30}{36}$ = $\frac{5}{6}$. Remaining = $\frac{1}{6}$. Time for A alone = ($\frac{1}{6}$)/($\frac{1}{12}$) = 2 hours. Total = 6+2 = 8 hours. But with both for 6 hrs: ($\frac{5}{36}$)×6 = $\frac{5}{6}$ filled. Remaining $\frac{1}{6}$ by A: 2 hours. Check: Total effective = 4 hours additional work needed.

Total distance = 240 + 360 = 600m. Time = 30 seconds. Speed = $\frac{600}{30}$ = 20 m/s = 20 × 3.6 = 72 km/h

Profit = 25% of 800 = 200. Selling Price = 800 + 200 = ₹1000

Upstream speed = 15-3 = 12 km/h. Downstream speed = 15+3 = 18 km/h. Time upstream = $\frac{36}{12}$ = 3 hours. Time downstream = $\frac{36}{18}$ = 2 hours. Total = 5 hours

SI = (P × R × T)/100 = (5000 × 8 × 2.5)/100 = $\frac{100000}{100}$ = ₹1000

Item 1: CP=500, SP=600 (20% gain). Item 2: CP=500, SP=425 (15% loss). Total CP=1000, Total SP=1025. Profit=25. Percentage = 2.5%

P's rate = $\frac{1}{30}$, Q's rate = $\frac{1}{40}$. Combined = $\frac{7}{120}$. In 10 days: 10 × $\frac{7}{120}$ = $\frac{7}{12}$ completed. Remaining = $\frac{5}{12}$. Q's time = ($\frac{5}{12}$)/($\frac{1}{40}$) = $\frac{5}{12}$ × 40 = 16.67 ≈ 15 days

A = P(1 + r/100)^n = 10000(1.1)^2 = 10000 × 1.21 = 12100. CI = 12100 - 10000 = ₹2100

Combined rate = $\frac{1}{6}$ + $\frac{1}{8}$ + $\frac{1}{10}$ = $\frac{20}{120}$ + $\frac{15}{120}$ + $\frac{12}{120}$ = $\frac{47}{120}$. Time = $\frac{120}{47}$ ≈ 2.73 hours

Let CP = 100. MP = 140. SP = 140 × $\frac{80}{100}$ = 112. Profit = 12%