198.20
163
Statements :
No man is a donkey. Rajesh is a man.
Conclusions :
I. Rajesh is not a donkey.
II. All men are not Rajesh.
E
4
Let and A and B are playing and A has 3$ and B won 3 times.
Total money earn by A = no of games A won – no of games A loss
if A loss game means B won.
Therefore
Total money earn by A = no of games A won – no of games B won
3 = no of games A won -3
no of games A won=6
So
A won = 6 games
B won = 3 games
Hence total no of games is 9
group wise work is use full and effectively
Ratio of diameters=1:2
Ratio of radius=1:2
Ratio of volumes=(4/3*3.14*r1^3)/(4/3*3.14*r2^3)
=r1^3/r2^3=1^3/2^3=1/8
1000
LNTKCHMF
All books can be arranged in 10! ways. A single pair of books can be taken as a unit and arranged among the 8 others in 9! ways. The pair of books can also be interchanged and therefore rearranged in 2! ways. Thus the probability of the pair always being together is (9!*2!)/10!
Let the number be 10Y+X
(10Y+X)/2 = (10X+Y)/3+6
(10Y+X)(1/2-1/3) = 6
10Y+X = 36
Therefore, sum of the digits = 3+6 = 9
Ans: 9
64
11
half and hour
Let’s assume the length of each train is ‘L’ and the speeds of the two trains are ‘V₁’ and ‘V₂’ respectively.
When the trains are moving in the opposite direction, their relative speed is the sum of their individual speeds. The total distance they need to cover is the sum of their lengths. Since they cross each other completely in 5 seconds, we can set up the following equation:
(V₁ + V₂) × 5 = 2L
When the trains are moving in the same direction, their relative speed is the difference between their individual speeds. The total distance they need to cover is the difference between their lengths. Since they cross each other completely in 15 seconds, we can set up the following equation:
(V₁ – V₂) × 15 = 2L
Now, let’s solve these equations to find the ratio of their speeds.
From the first equation, we have:
(V₁ + V₂) × 5 = 2L
V₁ + V₂ = (2L) / 5
From the second equation, we have:
(V₁ – V₂) × 15 = 2L
V₁ – V₂ = (2L) / 15
Let’s add these two equations together:
V₁ + V₂ + V₁ – V₂ = (2L) / 5 + (2L) / 15
2V₁ = (6L + 2L) / 15
2V₁ = (8L) / 15
V₁ = (4L) / 15
So, the speed of the first train is (4L) / 15.
Now, let’s substitute this value back into the first equation to find V₂:
(4L) / 15 + V₂ = (2L) / 5
V₂ = (2L) / 5 – (4L) / 15
V₂ = (6L – 4L) / 15
V₂ = (2L) / 15
Therefore, the speed of the second train is (2L) / 15.
The ratio of their speeds is given by:
(V₁ / V₂) = ((4L) / 15) / ((2L) / 15)
(V₁ / V₂) = 4L / 2L
(V₁ / V₂) = 2
So, the ratio of their speeds is 2:1.
speed of the train respect to man
= (63 – 3) km/hr
= 60 km/hr
= 60 * 1000 / 3600 m/sec
= 50/3 m/sec
time
= distance/speed
= 500 * 3/ 50
= 30 sec