# Recent questions tagged quantitative-aptitude 121
$\text{A}$ and $\text{B}$ are two points on a straight line. Ram runs from $\text{A}$ to $\text{B}$ while Rahim runs from $\text{B}$ to $\text{A}.$ After crossing each other, Ram and Rahim reach their destinations in one minute and four minutes, respectively. If they start at the same time, then the ratio of Ram’s speed to Rahim’s speed is $2$ $\sqrt{2}$ $2\sqrt{2}$ $\frac{1}{2}$
1 vote
122
For the same principal amount, the compound interest for two years at $5\%$ per annum exceeds the simple interest for three years at $3\%$ per annum by $\text{Rs } 1125.$ Then the principal amount in rupees is
123
In a group of $10$ students, the mean of the lowest $9$ scores is $42$ while the mean of the highest $9$ scores is $47.$ For the entire group of $10$ students, the maximum possible mean exceeds the minimum possible mean by $4$ $3$ $5$ $6$
1 vote
124
How many $3-$digit numbers are there, for which the product of their digits is more than $2$ but less than $7$?
1 vote
125
Veeru invested Rs $10000$ at $5\%$ simple annual interest, and exactly after two years, Joy invested Rs $8000$ at $10\%$ simple annual interest. How many years after Veeru’s investment, will their balances, i.e., principal plus accumulated interest, be equal?
1 vote
126
An alloy is prepared by mixing three metals $\text{A, B}$ and $\text{C}$ in the proportion $3:4:7$ by volume. Weights of the same volume of the metals $\text{A, B}$ and $\text{C}$ are in the ratio $5:2:6$. In $130$ kg of the alloy, the weight, in kg, of the metal $\text{C}$ is $70$ $96$ $48$ $84$
1 vote
127
On a rectangular metal sheet of area $135$ sq in, a circle is painted such that the circle touches two opposite sides. If the area of the sheet left unpainted is two$-$thirds of the painted area then the perimeter of the rectangle in inches is $5\sqrt{\pi }\left ( 3+\frac{9}{\pi} \right )$ ... $3\sqrt{\pi }\left ( 5+\frac{12}{\pi} \right )$ $4\sqrt{\pi }\left ( 3+\frac{9}{\pi} \right )$
128
If $\log_4 5=\left ( \log _{4}y \right )\left ( \log _{6}\sqrt{5} \right )$, then $y$ equals
1 vote
129
Two persons are walking beside a railway track at respective speeds of $2$ and $4$ km per hour in the same direction. A train came from behind them and crossed them in $90$ and $100$ seconds, respectively. The time, in seconds, taken by the train to cross an electric post is nearest to $87$ $82$ $75$ $78$
1 vote
130
The number of real$-$valued of the equation $2^{x}+2^{-x}=2-(x-2)^{2}$ is infinite $1$ $0$ $2$
1 vote
131
If $y$ is a negative number such that $2^{y^{2}\log _{2}3}=5^{\log_{2}3}$, then $y$ equals $\log _{2}\left ( \frac{1}{3} \right )$ $-\log _{2}\left ( \frac{1}{3} \right )$ $\log _{2}\left ( \frac{1}{5} \right )$ $-\log _{2}\left ( \frac{1}{5} \right )$
1 vote
132
How many distinct positive integer-valued solutions exist to the equation $\left ( x^{2}-7x+11 \right )^{(x^{2}-13x+42)} =1$? $6$ $8$ $2$ $4$
1 vote
133
A person spent Rs $50000$ to produce a desktop computer and a laptop computer. He sold the desktop at $20\%$ profit and the laptop at $10\%$ loss. If overall he made a $2\%$ profit then the purchase price, in rupees, of the desktop is
1 vote
134
The area of the region satisfying the inequilities $\left | x \right |-y\leq 1,y\geq 0$ and $y\leq 1$ is
1 vote
135
A straight road connects points $\text{A}$ and $\text{B}$. Car $1$ travels from $\text{A}$ to $\text{B}$ and Car $2$ travels from $\text{B}$ to $\text{A}$, both leaving at the same time. After meeting each other, they take $45$ minutes and $20$ minutes, respectively, to complete their ... . If Car $1$ travels at the speed of $60$ km/hr, then the speed of Car $2$, in km/hr, is $90$ $100$ $80$ $70$
1 vote
136
Among $100$ students, $x_{1}$ have birthdays in January, $x_{2}$ have birthdays in February, and so on. If $x_{0}= \text{max}\left ( x_{1},x_{2},\dots,x_{12} \right ),$ then the smallest possible value of $x_{0}$ is $9$ $10$ $8$ $12$
1 vote
137
The mean of all $4-$digit even natural numbers of the form $`aabb\text{’},$ where $a>0,$ is $5050$ $4466$ $5544$ $4864$
1 vote
138
Leaving home at the same time, Amal reaches office at $10:15$ am if he travels at $8$ km/hr, and at $9:40$ am if he travels at $15$ km/hr. Leaving home at $9:10$ am, at what speed, in km/hr, must he travel so as to reach office exactly at $10$ am? $13$ $14$ $12$ $11$
1 vote
139
A train travelled at one$-$thirds of its usual speed, and hence reached the destination $30$ minutes after the scheduled time. On its return journey, the train initially travelled at its usual speed for $5$ minutes but then stopped for $4$ minutes for an emergency. The ... now increase its usual speed so as to reach the destination at the scheduled time, is nearest to $58$ $67$ $61$ $50$
140
If $x=\left ( 4096 \right )^{7+4\sqrt{3}}$, then which of the following equals $64$? $\frac{x^{7}}{x^{2\sqrt{3}}}$ $\frac{x^{7}}{x^{4\sqrt{3}}}$ $\frac{x\frac{7}{2}}{x\frac{4}{\sqrt{3}}}$ $\frac{x\frac{7}{2}}{x^{2\sqrt{3}}}$
1 vote
141
If $f\left ( 5+x \right )= f\left ( 5-x \right )$ for every real $x,$ and $f\left ( x \right )=0$ has four distinct real roots, then the sum of these roots is $0$ $40$ $10$ $20$
1 vote
142
If $a, b$ and $c$ are positive integers such that $ab=432, bc=96$ and $c<9,$ then the smallest possible value of $a+b+c$ is $56$ $59$ $49$ $46$
1 vote
143
In a group of people, $28\%$ of the members are young while the rest are old. If $65\%$ of the members are literates, and $25\%$ of the literates are young, then the percentage of old people among the illiterates is nearest to $62$ $55$ $66$ $59$
1 vote
144
A circle is inscribed in a thombus with diagonals $12$ cm and $16$ cm. The ratio of the area of circle to the area of rhombus is $\frac{5\pi }{18}$ $\frac{6\pi }{25}$ $\frac{3\pi }{25}$ $\frac{2\pi }{15}$
1 vote
145
A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of the remaining stock along with one extra to the second and continues giving away in this fashion. His total stock exhausts after he takes care of $5$ children. How many toffees were there in his stock initially?
146
Let $\text{A, B}$ and $\text{C}$ be three positive integers such that the sum of $\text{A}$ and the mean of $\text{B}$ and $\text{C}$ is $5$. In addition, the sum of $\text{B}$ and the mean of $\text{A}$ and $\text{C}$ is $7$. Then the sum of $\text{A}$ and $\text{B}$ is $6$ $5$ $7$ $4$
1 vote
147
A solution, of volume $40$ litres, has dye and water in the proportion $2:3.$ Water is added to the solution to change this proportion to $2:5.$ If one$-$ fourths of this diluted solution is taken out, how many litres of dye must be added to the remaining solution to bring the proportion back to $2:3$?
1 vote
148
The number of distinct real roots of the equation $\left ( x+\frac{1}{x}\right )^{2}-3\left ( x+\frac{1}{x} \right )+2= 0$ equals
1 vote
149
A solid right circular cone of height $27$ cm is cut into two pieces along a plane parallel to its base at a height of $18$ cm from the base. If the difference in volume of the two pieces is $225$ cc, the volume, in cc, of the original cone is $232$ $256$ $264$ $243$
150
151
A man rowed $3$ miles upstream in $90$ minutes. If the river flowed with a current of $2$ miles per hour, how long did the man’s return trip take? $20$ minutes $30$ minutes $45$ minutes $60$ minutes
152
A circular garden twenty feet in diameter is surrounded by a path three feet wide. What is the area of the path? $51 \pi$ square feet $60 \pi$ square feet $69 \pi$ square feet $90 \pi$ square feet
153
A man walks $10$ miles at an average rate of $2$ miles per hour and returns on a bicycle at an average rate of $10$ miles per hour. How long (to the nearest hour) does the entire trip take him? $4$ hours $5$ hours $6$ hours $7$ hours
154
What is the area of a semicircle with a diameter of $16$ inches? $32 \pi$ square inches $64 \pi$ square inches $128 \pi$ square inches $256 \pi$ square inches
155
Which of the following figures has the largest perimeter $(1 \text{ foot} = 12 \text{ inches})$ a square with a diagonal of $5$ feet a rectangle with sides of $3$ feet and $4$ feet an equilateral triangle with a side equal to $48$ inches a regular hexagon whose longest diagonal is $6$ feet
156
Two bicyclists travel in opposite directions. One travels $5$ miles per hour faster than the other. In $2$ hours they are $50$ miles apart. What is the rate of the faster bicyclist? $11.25$ mph $15$ mph $20$ mph $22.5$ mph
157
Rani will be twice Raja’s age in $3$ years when Raja will be $40$. How many years old is Rani now? $20$ $80$ $77$ $37$
1 vote
A certain number when added to $50\%$ of itself is $27$. What is the number? $7$ $9$ $11$ $18$
Twelve less than $4$ times a number is $20$. What is the number? $2$ $4$ $6$ $8$
The sum of a number and its double is $69$. What is the number? $46.6$ $34.5$ $23$ $20$