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.

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.

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)**

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

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

Fill rate = $\frac{1}{20}$, Drain rate = $\frac{1}{30}$. Net rate = $\frac{1}{20}$ - $\frac{1}{30}$ = $\frac{3}{60}$ - $\frac{2}{60}$ = $\frac{1}{60}$. Time = 60 minutes

Let original = x. x × 1.15 = 299. x = $\frac{299}{1}$.15 = 260

CP per banana = $\frac{30}{12}$ = 2.5. SP per banana = 3. Profit = 0.5. Percentage = (0.$\frac{5}{2}$.5) × 100 = 20%

Work done by A in 1 day = $\frac{1}{20}$. Work done by A+B in 1 day = $\frac{1}{12}$. So B's work in 1 day = $\frac{1}{12}$ - $\frac{1}{20}$ = (5-3)/60 = $\frac{2}{60}$ = $\frac{1}{30}$. Therefore B takes 30 days.

Filling rate = $\frac{1}{15}$ per hour. Emptying rate = $\frac{1}{20}$ per hour. Net rate = $\frac{1}{15}$ - $\frac{1}{20}$ = (4-3)/60 = $\frac{1}{60}$. Time = 60 hours.

Total cost for A = 500 × 24 = ₹12,000. Total cost for B = 600 × 18 = ₹10,800. B costs less, so B is more cost-effective.

Downstream speed = $\frac{60}{3}$ = 20 km/h. Upstream speed = $\frac{60}{4}$ = 15 km/h. Speed of boat = (20+15)/2 = $\frac{35}{2}$ = 17.5 km/h.

SI = (P × R × T)/100 = (10000 × 10 × 3)/100 = 3000. Amount = 10000 + 3000 = ₹13,000.

Total distance = train length + platform length = 200 + 400 = 600m. Speed = $\frac{600}{30}$ = 20 m/s.

Profit = 1000 - 800 = ₹200. Profit% = ($\frac{200}{800}$) × 100 = 25%.