There are 13 hearts and 3 more kings
? p (heart or a king ) = (13 + 3)/52 = 4/13
? P (neither a heart nor a king) = 1 - 4/13 = 9/13
Let the length of the train be 'L' meters and its speed be 'v' meters/sec
Then, L/v = 15
? v = L/15 ....(1)
Now, (L + 100)/25 = L/15
? L = 150 m
CP of 1 toffee for 1st rate = 1/6
CP of 1 toffee for 2nd rate = 1/7
CP of 2 toffee after mixing = 1/6 + 1/7 = 13/42
CP of 1 toffee after mixing = 13/84
SP of 1 toffee after mixing = 1/6
Gain = 1/6 - 13/84 = 1/84
Gain% = [(1/84) / (13/84)] x 100% = 100/13% = 79/13%
Here n = 120, a = 35, x = 39, y = 15
Number of students passed = n (a - y)/(x - y)
= 120(35 - 15)/(39 -15)
= 100 students passed
Let the fraction be x / y.
According to the question,
( x+2)/(y+1) = 1/2
? 2x + 4 = y+1
? 2x - y = -3 .........................(i)
Again according to the question,
(x+1)/(y-2) = 3/5
? 5x +5 = 3y - 6
? 5x - 3y = -11..........................(ii)
on multiplying Eq. (i) by 3 and then subtracting from Eq. (ii) we get,
multiplying Eq. (i) by 3
6x - 3y = -9
subtracting from Eq. (ii)
5x- 3y - ( 6x - 3y ) = -11 - (-9)
5x- 3y - 6x + 3y = -11 + 9
- x = - 2
x= 2
On putting the value of x in Eq. (i) we get
2x- y = -3
2 x 2 - y = -3
? 2 x 2 -y = -3
? -y = -3 - 4
? y = 7
? Original fraction = x/y =2/7
Here, average decreases by 3 months of 3/12 yr.
Sum of ages decreased
= 30 x 3/12 = 15/2 = 7.5 yr
? Age of priyanka = (25 - 7.5) = 17.5 yr.
Let the number of students in the class = N
According to the question,
(35N + 6 x 33) / (N + 6) = 35 - (1/2)
? 35N + 198 = 34.5 (N + 6)
? 35N +198 = 34.5N + 207
? 0.5N = 207 -198N = 9/0.5 = 18
? N = 18 days
Sum of 14 girls and teacher age = 15 x 15 = 225
Without teacher's age sum of 14 girls age = 14 x 14 = 196
? Teacher's age = 225 -196 = 29 year
Length of platform is not given. it can not be determined.
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