List of top Quantitative Aptitude Questions

A vessel has a milk solution in which milk and water are in the ratio 4:1. By addition of water to it, milk solution with milk and water in the ratio 4:3 was formed. On replacing 14 L of this solution with pure milk, the ratio of milk and water changed to 5:3. What is the volume of the water added?

If $3x + 4y = 12$ and $x - y = 1$, what is the value of $x + y$? 
 

What is the number of solutions to $|x - 2| = |x - 4|$? 
 

In the figure, \( OABC \) is a parallelogram. The area of the parallelogram is 21. Coordinates are: \( O = (0,0) \), \( A = (7,0) \), and point \( C \) lies on line \( x = 3 \). Find coordinates of \( B \).

What is the probability that a leap year has 53 Sundays? 
 

If \( \log_x(a - b) - \log_x(a + b) = \log_x\left(\frac{b}{a}\right) \), find \( \frac{a^2 + b^2}{b^2 + a^2} \)

A boat travels 24 km upstream in 6 hours and 30 km downstream in 5 hours. What is the speed of the boat in still water? 
 

If $x^2 + y^2 = 25$ and $xy = 12$, what is $x + y$? 
 

What is the sum of the series $1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \ldots$? 
 

Letters of the word “ATTRACT” are written on cards and kept on a table. Manish lifts three cards at a time, writes all possible combinations of the three letters on a piece of paper, and then replaces the cards. He is to strike out all the words which look the same when seen in a mirror. How many words is he left with?
If the roots of the equation \[ (a^2 + b^2)x^2 + 2(b^2 + c^2)x + (b^2 + c^2) = 0 \] are real, which of the following must hold true?

What is the value of $\sqrt{50 + \sqrt{50 + \sqrt{50 + \ldots}}}$? 
 

A number when divided by 7 leaves a remainder of 4. What is the remainder when its square is divided by 7? 
 

In how many ways can 6 people be seated around a circular table? 
 

A car travels at 60 km/h for half the distance and 80 km/h for the other half. What is the average speed for the entire journey? 
 

What is the value of x if:

2x · 3x+1 = 3888

Let \( a_1, a_2, a_3, \dots \) be terms on A.P. If \[ a_1 + a_2 + \dots + a_p = p^2, \, p \neq q, \, \text{then} \, a_q = \frac{p^2}{q^2} \] Then \( a_q \) equals:
Train A running at $60$ km/h leaves Mumbai for Delhi at $6$ p.m. Train B running at $90$ km/h also leaves for Delhi at $9$ p.m. Train C leaves Delhi for Mumbai at $9$ p.m. If all three trains meet at the same time between Mumbai and Delhi (distance $=1260$ km), find the speed of Train C.
Rahul starts a business with ₹ 8000. After $6$ months, Sanjay joins with some capital. If their profits after one year are equal, find Sanjay's investment.
A watch is bought for ₹ 1950 in cash and sold for ₹ 2200 on one-year credit. If the interest rate is $10\%$ p.a., find the trader's gain/loss.
In an express train, the numbers of passengers travelling in A.C. Sleeper Class, First Class and Sleeper Class are in the ratio $1:2:3$, and the fares of these classes are in the ratio $5:4:2$. If the total income from the train is ₹ 54000, find the income from the A.C. Sleeper Class.
A private telephone company serving a small community makes a profit of ₹ 12 per subscriber, if it has 725 subscribers. It decides to reduce the rate by a fixed sum for each subscriber over 725, thereby reducing the profit by 1 paise per subscriber. Thus, there will be profit of ₹ 11.99 on each of the 726 subscribers, ₹ 11.98 on each of the 727 subscribers etc. The number of subscribers which will give the company, the maximum profit, is:
The values of the numbers \(2^{2004}\) and \(5^{2004}\) are written one after another. How many digits are there in all?
There are two water drums in my house whose volumes are in the ratio \(1 : 5\). Every day the smaller drum is filled first and then the same pipe is used to fill the bigger drum. Normally by 1:30 pm the smaller drum would just be full. But today, I returned early and started drawing water manually. I poured one-third into the smaller drum and the rest into the bigger drum. I continued this till the smaller drum was full. Immediately after that, I shifted the pipe into the bigger drum. If today the bigger drum was filled 12 minutes earlier than the normal time, when was the smaller drum full?
Two cars \(A\) and \(B\) start from two points \(P\) and \(Q\) respectively towards each other simultaneously. After travelling some distance, at a point \(R\), car \(A\) develops engine trouble. It continues to travel at \(2/3\)rd of its usual speed to meet car \(B\) at point \(S\) where \(PR = QS\). If the engine trouble had occurred after car \(A\) had travelled double the distance it would have met car \(B\) at a point \(T\) where \(ST = SQ/9\). Find the ratio of speeds of \(A\) and \(B\).