# Recent questions and answers in Quantitative Aptitude

1
How many litres of a $3\%$ hydrogen peroxide solution should be mixed with $6$ liters of a $30\%$ hydrogen peroxide solution so as to get a mixture of $12\%$ solution ? $3$ litres $6$ liters $9$ litres $12$ litres
2
A train travelling from Delhi to Ambala meets with an accident after $1$ hr. It is stopped for $\frac{1}{2}$ hr, after which it proceeds at fourth-fifth of its usual rate, arriving at Ambala at $2$ hr late. If the train has covered $80$ km more before the accident, it would have been just $1$ hr late. The usual speed of the train is : $20$ km/hr $30$ km/hr $40$ km/hr $50$ km/hr
3
A train enters into a tunnel $AB$ at $A$ and exits at $B$. A jackal is sitting at $O$ in another by passing tunnel $AOB$, which is connected to $AB$ at $A$ and $B$, where $OA$ is perpendicular to $OB$. A cat is sitting at $P$ inside the tunnel $AB$ making the shortest possible distance ... $A$. The ratio of speeds of jackal and cat is : $\frac{2}{3}$ $\frac{4}{3}$ $\frac{5}{3}$ $\frac{3}{2}$
4
For the word given at the top of each table, match the dictionary definitions on the left (A, B, C, D) with their corresponding usage on the right (E, F, G, H). Out of the four possibilities given in the boxes below the table, select the one that has all the definitions and their usages correctly matched. EXCEED Dictionary ... C-E, D-G A-H, B-E, C-F, D-G A-G, B-F, C-E, D-H A-F, B-G, C-H, D-E
5
Let $A$ and $B$ be two regular polygons having $a$ and $b$ sides, respectively. If $b= 2a$ and each interior angle of $B$ is $3/2$ times each interior angle of $A$, then each interior angle, in degrees, of a regular polygon with $a + b$ sides is_____
6
Let $A$ be a real number. Then the roots of the equation $x^{2}-4x-\log _{2}A=0$ are real and distinct if and only if $A> \frac{1}{16}$ $A> \frac{1}{8}$ $A< \frac{1}{16}$ $A< \frac{1}{8}$
1 vote
7
A can contains a mixture of two liquids $A$ and $B$ in proportion $7:5$. When $9$ litres of mixture are drawn off and the can is filled with $B$, the proportion of $A$ and $B$ becomes $7:9$. How many litres of liquid $A$ was contained by the can initially? $25$ $10$ $20$ $21$
1 vote
8
If $a^{2}+b^{2}+c^{2}=1$, then which of the following can't be the value of $ab+bc+ca$ ? $0$ $\frac{1}{2}$ $\frac{-1}{4}$ $-1$
9
The sum of first $n$ terms of an $A.P$. whose first term is $\pi$ is zero. The sum of next $m$ terms is : $\frac{ \pi m \left(m+n \right)}{n-1}$ $\frac{ \pi n \left(m+n \right)}{1-n}$ $\frac{ \pi m \left(m+n \right)}{1-n}$ $1$
10
A cylindrical box of radius $5$ cm contains $10$ solid spherical balls each of radius $5$ cm. If the topmost ball touches the upper cover of the box, then the volume of the empty space in the box is: $\dfrac{2500\pi}{3}$ cubic cm $500\pi$ cubic cm $2500\pi$ cubic cm $\dfrac{5000\pi}{3}$ cubic cm
11
The value of the following expression : $\left [ \frac{1}{2^{2}-1} \right ]+\left [ \frac{1}{4^{2}-1} \right ]+\left [ \frac{1}{6^{2}-1} \right ]+\dots\dots+\left [ \frac{1}{20^{2}-1} \right ]$ is : $\frac{10}{21}$ $\frac{13}{27}$ $\frac{15}{22}$ $\frac{22}{15}$
12
Find the value of the expression $1-6+2-7+3-8+\dots\dots$ to $100$ terms. $-250$ $-500$ $-450$ $-300$
13
Adrian starts a start-up with a capital of Rs. $85,000.$ Brian joins in the start-up with Rs. $42,500$ after sometime. For how much period does Brian join, if the profits at the end of the year are divided in the ratio of $3:1?$ $5$ months $6$ months $7$ months $8$ months
14
The minute hand is $10$ cm long. Find the area of the face of the clock described by the minute hand between $9$ a.m and $9:35$ a.m. ${183.3\ cm^{2}}$ ${366.6\ cm^{2}}$ ${244.4\ cm^{2}}$ ${188.39\ cm^{2}}$
15
The price of an article was increased by $p\%$, later the new price was decreased by $p\%$. If the last price was Re. $1$ then the original price was: $\dfrac{1-p^{2}}{200}\\$ $\dfrac{\sqrt{1-p^{2}}}{100} \\$ $1-\dfrac{p^{2}}{10,000-p^{2}} \\$ $\dfrac{10,000}{10,000-p^{2}}$
16
What is the largest positive integer $n$ such that $\frac{n^{2}+7n+12}{n^{2}-n-12}$ is also a positive integer? $8$ $12$ $16$ $6$
17
The quadratic equation $x^{2}+bx+c=0$ has two roots $4a$ and $3a$, where a is an integer. Which of the following is a possible value of $b^{2}+c$? $3721$ $549$ $427$ $361$
18
A cyclist leaves $A$ at $10$ am and reaches $B$ at $11$ am. Starting from $10:01$ am, every minute a motor cycle leaves $A$ and moves towards $B$. Forty-five such motor cycles reach $B$ by $11$ am. All motor cycles have the same speed. If the cyclist had doubled his speed, how many motor cycles would have reached $B$ by the time the cyclist reached $B$? $23$ $20$ $15$ $22$
19
Two ants $A$ and $B$ start from a point $P$ on a circle at the same time, with $A$ moving clock-wise and $B$ moving anti-clockwise. They meet for the first time at $10:00$ am when $A$ has covered $60$% of the track. If $A$ returns to $P$ at $10:12$ am, then $B$ returns to $P$ at $10:25$am $10:18$am $10:27$am $10:45$am
20
John jogs on track A at $6$ kmph and Mary jogs on track $B$ at $7.5$ kmph. The total length of tracks $A$ and $B$ is $325$ metres. While John makes $9$ rounds of track $A$, Mary makes $5$ rounds of track $B$. In how many seconds will Mary make one round of track $A$?______
21
The salaries of Ramesh, Ganesh and Rajesh were in the ratio $6:5:7$ in $2010$, and in the ratio $3:4:3$ in $2015$. If Ramesh’s salary increased by $25$% during $2010-2015$, then the percentage increase in Rajesh’s salary during this period is closest to $8$ $7$ $9$ $10$
22
If x is a real number, then $\sqrt{\log _{e}\frac{4x-x^{2}}{3}}$ is a real number if and only if $1\leq x\leq 2$ $-3\leq x\leq 3$ $1\leq x\leq 3$ $-1\leq x\leq 3$
23
In an examination, Rama's score was one-twelfth of the sum of the scores of Mohan and Anjali. After a review, the score of each of them increased by $6$. The revised scores of Anjali, Mohan, and Rama were in the ratio $11:10:3$. Then Anjali's score exceeded Rama's score by $24$ $26$ $32$ $35$
24
A dishonest milkman professes to sell his milk at $C.P$. but he mixes it with water and thereby gains $25\%$. The percentage of water in the mixture is : $25\%$ $20\%$ $4\%$ None of these
25
A boy $1.4$ $m$ tall casts a shadow $1.2$ $m$ long at the time when a building casts a shadow $5.4$ $m$ long. The height of the building is: $4.63 m$ $3.21 m$ $6.3 m$ $5.6 m$
26
Two persons start walking on a road that diverge at an angle of $120^{\circ}$. If they walk at the rate of $3$km/h and $2$km/h respectively. Find the distance between them after $4$hrs. $4\sqrt{19}$ km $5$ km $7$ km $8\sqrt{19}$ km
27
The expressions $\dfrac{\tan A}{1-\cot A}+\dfrac{\cot A}{1-\tan A}$ can be written as: $\sin A \ \cos A+1$ $\sec A \ cosec A+1$ $\tan A+ \cot A+1$ $\sec A +cosec A$
28
The line $x+y=4$ divides the line joining $\text{(-1,1) & (5,7)}$ in the ratio $\lambda : 1$ then the value of $\lambda$ is: $2$ $3$ $\dfrac{1}{2}$ $1$
1 vote
29
A flagstaff $17.5$ m high casts a shadow of length $40.25$ m. The height of the building, which casts a shadow of length $28.75$ m under similar condition will be? $10$ m $12.5$ m $17.5$ m $21.25$ m
30
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
31
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
32
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
33
Let x, y and z be distinct integers, that are odd and positive. Which one of the following statements cannot be true? $xyz^2$ is odd. $(x − y)^2 z$ is even. $(x + y − z)^2 (x + y)$ is even. $(x − y) (y + z) (x + y − z)$ is odd
1 vote
34
In an acute angled triangle $ABC$, if $\tan \left(A+B-C \right)=1$ and $\sec \left(B+C-A \right)=2$, Find angle $A$. $60^\circ$ $45^\circ$ $30^\circ$ $90^\circ$
35
$\left [\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^{2}}+\frac{4}{1+x^{4}}+\frac{8}{1+x^{8}} \right ]$ equal to : $1$ $0$ $\frac{8}{1-x^{8}}$ $\frac{16}{1-x^{16}}$
1 vote
36
A two digit number is such that the product of the digits is $8$. When $18$ is added to the number, the digits are reversed. The number is : $18$ $24$ $81$ $42$
Find the mode of the following data : $\begin{array}{|cl|cI|}\hline &\text{Age} & \text{0-6} & \text{6-12} & \text{12-18} & \text{18-24} & \text{24-30} & \text{30-36} & \text{36-42} \\ \hline &\text{Frequency} & \text{6} & \text{11} & \text{25} & \text{35} & \text{18} & \text{12} & \text{6} \\ \hline \end{array}$ $20.22$ $19.47$ $21.12$ $20.14$