CDS 2026 Quantitative Aptitude Medium Questions

X is an alloy of copper and zinc. Y is an alloy containing 80% of copper, 4% of zinc and 16% of tin. A fused mass of X and Y is found to contain 74% of copper, 16% of zinc and 10% of tin. What is the percentage of copper in X ?

Eight men and 24 women can finish a piece of work in one day while 12 men and 18 women can also finish it in one day. What is the time taken by 24 men and 72 women to finish the work ?

$27^{27}-9^{40}-3^{79}$ is divisible by how many natural numbers less than $10$?

The HCF and LCM of two numbers $p$ and $q$ are $44$ and $4620$ respectively. When $p$ is divided by $55$, the quotient is $4$ and remainder is $0$. What is the value of $q$?

Seven times a two-digit positive number is equal to four times the number obtained by reversing the order of the digits. How many such two-digit numbers are there ?

In what duration of time will ₹3300 become ₹3399 at 12% per annum interest compounded quarterly ?

Two numbers P and Q are such that P : Q = x : y. If 1 is added to both the numbers, the ratio becomes 7 : 10. If 3 is added to both the numbers, the ratio becomes 3 : 4. What is $(x+y):(x-y)$ equal to ?

The ratio of the present age of X to that of Y is $4:5$. $k$ (less than 10) years ago, this ratio was $1:2$. How many values of $k$ are possible if the ages are expressed in complete years?

The diameter of a copper solid sphere is 6 cm. The sphere is melted and recast into a wire. If the diameter of the wire is 0.5 cm, then what is the length of the wire?

12 men working 8 hours a day can completely build a wall of length 100 m, breadth 20 cm and height 5 m in 10 days. How many days will 16 men working 10 hours a day require to build a wall of length 200 m, breadth 60 cm and height 5 m ?

A metallic sheet of rectangular shape is $48\text{cm}\times 36\text{cm}$. From each corner a square of side $x\text{cm}$ is cut off and an open box is made of the remaining sheet. If the box holds $5.12$ litre of water, then what is the value of $x$?

A single discount which is equivalent to a series of discounts $p\%$, $\frac{p}{2}\%$, $\frac{p}{4}\%$ is $31.6\%$. What is the value of $p$ ?

A person goes downstream at $x$km/h and upstream at $y$km/h by the same boat. What is the ratio of speed of boat in still water to speed of water?

The arithmetic mean of 100 observations is 50. If 10 is added to each observation then what will be the new arithmetic mean ?

X can do a piece of work in 4 days and Y can do the same piece of work in 6 days. Which of the following statements is/are correct ?

I. If X and Y work alternately starting with X, then the piece of work will be finished on the fifth day.

II. If X and Y work alternately starting with Y, then the piece of work will be finished in less than 5 days.

Select the answer using the code given below :

What is the greatest possible speed at which a person can walk $13.3\text{km}$ and $20.9\text{km}$ so that the time (in hours) required in each case is a whole number?

A train P starts from station X for station Y and another train Q starts from station Y for station X at the same time. After passing each other, P takes 4 hours to reach Y and Q takes 1 hour to reach X. If the average speed of P is 60 km/h, then what is the average speed of Q ?

What is the sum of all the divisors of $256$?

What is the digit in the unit place of the number $1^1\times 3^3\times 5^5\times 7^7\times 9^9$ ?

Without stoppages, a train travels at an average speed of $60$km/h and with stoppages it covers the same distance at an average speed of $48$km/h. How many minutes per hour does the train stop?