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The first 10 odd prime numbers are 3, 5, 7, 11, 13, 17, 19, 23, 29 and 31.
Sum of the odd prime numbers = (3+5+7+11+13+17+19+23+29+31)
= 158
Number of odd prime numbers = 10
We know, Average = (sum of the 10 odd prime numbers ÷ Number of odd
prime numbers)
Average =
= 15.8
∴ The Average of first 10 prime numbers which are odd is 15.8
23
Before Swapping
_ _ _ _ _ _ _ Shilpa ……..Reena _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
After Swapping
_ _ _ _ _ _ _ Reena _ _ _ _ _ Shilpa _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
—————————–>14=17 <——————————-
So total number of girls in that row are 30
The formula to find number of diagonals (D) given total number of vertices or sides (N) is
N * (N – 3)
D = ———–
2
Using the formula, we get
1325 * 2 = N * (N – 3)
N2 – 3N – 2650 = 0
Solving the quadratic equation, we get N = 53 or -50
It is obvious that answer is 53 as number of vertices can not be negative.
Alternatively, you can derive the formula as triange has 0 diagonals, quadrangel has 2, pentagon has 5, hexagon has 9 and so on……
Hence the series is 0, 0, 0, 2, 5, 9, 14, …….. (as diagram with 1,2 or 3 vertices will have 0 diagonals).
Using the series one can arrive to the formula given above.
Ans. let x is distance from A to B
and y is initial speed.
30/y+(x-30)5/4y -x/y = 3/4
=> 4x-12y=120 —-(1).
45/y + (x-45)5/4y -x/y=3/5
=> 5x-12y=225 ——-(2).
From equ (1) and equ (2) we will get.
x=25 and y=105
so initial speed is 25 km/hr
and Distance From A to B is 105 km
1(100-1)+ 2(100-2)+…..99(100-99)
N=100
solution: N(N-1)
100(99)= 9900
1/x=1/5+1/10+1/30=lcm is 30.
->30/5=6
->30/10=3
->30/30=1
1/x=6+3+1=10
1/x=10/30=1/3=x=3
Ans is 3 hr.
If the bell rung when they r started is also counted then it
will be 5 otherwise 4