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There are 9 students in a classroom. If each student shakes hands just once with everyone else, total how many handshakes take place?
In a group of \(n\) people, number of handshakes \(=n(n-1) / 2\).
How many 3-digit numbers can you make using the digits 4, 5, and 6?
We have 3 choices for the first digit, 2 choices for the second digit, and 1 choice for the third digit. The total number of 3-digit numbers is given by 3 x 2 x 1 = 6.
How many different words can we make using the letters L, I, V, and E without repeating the letters?
Anjali goes to College at \(20 \mathrm{~km} / \mathrm{h}\) and reaches college 4 minutes late. Next time she goes at 25 \(\mathrm{km} / \mathrm{h}\) and reaches the college 2 minutes earlier than the scheduled time. What is the distance of her school in km?
Find the missing number: 62, 64, ? , 32, 14,16
\((x-2)\) person can do a work in \(x\) days and \((x+7)\) person can do \(75 \%\) of the same work in (x – 10)days. Then in how many days can \((x+10)\) person finish the work?
\(
\begin{aligned}
&\frac{3}{4} \times(x-2) x=(x+7)(x-10) \\
&\Rightarrow x^{2}-6 x-280=0 \\
&\Rightarrow \mathrm{x}=20 \text { and } \mathrm{x}=-14
\end{aligned}
\)
so, the acceptable values is \(x=20\)
Therefore, Total work \(=(x-2) x=18 \times 20=360\) unit
Now \(360=30 \times n\)
\(
\Rightarrow n=12 \text { days }
\)
Sruthi, Swetha, and Swati together can cut 216 Apples of the same size in 3 hours. The number of Apples cut by Sruthi in 9 hours is the same as the number of Apples cut by Swati in 7 hours. In one hour, Swati can cut as many Apples more than Swetha as Swetha can cut more than Sruthi. Then the number of Apples cut by Swetha in one hour?
\(\begin{aligned}
&U+V+W=72 \\
&9 U=7 W \\
&W-V=V-U \\
&V=24
\end{aligned}\)
Today is Monday. After 60 days, it will be:
A train leaves Meerut at 5 a.m. and reaches Delhi at 9 a.m. Another train leaves Delhi at 7 a.m. and reaches Meerut at 10.30 a.m. At what time do the two trains cross each other?
The first train takes 4 hours and the second train takes 3.5 hours.
The time ratio is 8: 7. Therefore, the speed ratio will be 7: 8.
Let the speeds be \(7 x\) and \(8 x\), and distance is \(28 x(4 \times 7\) or \(3.5 \times 8)\).
At \(7 \mathrm{AM}\), the first train must have covered a distance of \(14 \mathrm{x}\). Therefore, at \(7 \mathrm{~A}\) M. The distance between the two trains is \(28 \mathrm{x}-14 \mathrm{x}=14 \mathrm{x}\).
Time taken to meet \(=14 x /(7 x+8 x)=14 / 15\) hour or 56 minutes.
Hence, the two trains meet at 7.56 AM.
If 5 men take an hour to dig a ditch, then how long should 12 men take a dig to the ditch of the same type?
\(\mathrm{M} 1 \mathrm{H} 1=\mathrm{M} 2 \mathrm{H} 2\)
\(
5^{*} 60=12^{*} \mathrm{H} 2
\)
\(
\mathrm{H} 2=25 \mathrm{~min}
\)
How many times are the hands of a clock at the right angle in a day?
\(\text { In } 12 \text { hours, they are at right angles } 22 \text { times. In } 24 \text { hours, they are at right angles } 44 \text { times. }\)
Look at this series: 14, 28, 20, 40, 32, 64, 56, ? What number is missing in the series?
\(\text { This is an alternating multiplication and subtracting series: First, multiply by } 2 \text { and then subtract } 8 \text {. }\)
What number should come next in the series: 53, 53, 40, 40, 27, 27, 14 ___?
In this series, each number is repeated, then 13 is subtracted to arrive at the next number.
There was a cycle race going on. 1/5th of those in front of a person and 5/6 of those behind him gives the total number of participants. How many people took part in the race?
Some students planned a picnic. The budget for food was Rs. 500. But, 5 of them failed to go and thus the cost of food for each member increased by Rs. 5. How many students attended the picnic?
The average score of boys in an examination in a school is 71 and that of the girls is 73. The average score of the school is 71.8. The ratio of the number of boys to that of the girls that appeared in the examination is
\(
\begin{aligned}
&71.8=(71 x+73 y) /(x+y) \\
&71.8(x+y)=71 x+73 y \\
&0.8 x=1.2 y
\end{aligned}
\)
\(x: y=12: 8\) which is equals to \(3: 2\)
Students of Loyola college are lined up in a row. Lata who is standing 16th from the left stands on the immediate right of Sita. When they exchange their places, Sita stands 14th from the right. Find out the total number of students in the row.
\(\text { Number of students in the row }=15+14=29\)
A man travels 40 Km by bicycle and 20 Km by walk in 42 minutes. Instead, if he covers 25 Km by bicycle and 35 Km by walk, he takes 18 more minutes. What is his speed on a bicycle in Kmph?
Let the speed of the man by bicycle be b and walk be \(w\) in Kmph respectively.
According to the question, \((40 / b)+(20 / w)=(42 / 60)\)
\(
(25 / b)+(35 / w)=1
\)
Solving for \(b\) and \(w\), we get the value of \(b\) as \(200 \mathrm{Kmph}\).
A shopkeeper marks an article at \(40 \%\) higher price than the cost price and offers a discount of \(25 \%\). What is the actual profit percentage of the shopkeeper?
Let the cost price of article be \(x\)
Marked Price \(=1.4 x\)
Selling Price \(=1.4 x \times 0.75=1.05 x\)
Hence, the profit percentage \(=5 \%\)
\(\text { If } 1+4=5,2+5=12,3+6=21,5+8=?\)
\(5+8=45 \text { can be written as } 5 \times(1+8)=45\)
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