Let x be the length of the standing train
? Speed of the train = (500 + x)/20
? 100 x (5/18) = (500 + x)/20
? 500 + x = (100 x 5 x 20)/18
? 500 + x = 555.56
? x = 555.56 - 500 = 55.56 m
A non-leap year has 365 days, each day repeats for 52 times with 1 day left
This one can be {Sun, Mon, Wed, Thu, Fri, and Sat}.
? p = 6/7
Given expression = 15/2 -[9/4 ÷ {5/4 - 1/2(3/2 - 1/3 - 1/6)}]
= 15/2 -[9/4 ÷ {5/4 - 1/2 x 1}]
= 15/2 -[9/4 ÷ {5/4 - 1/2}]
= 15/2 -[9/4 ÷ 3/4] = 15/2 - [9/4 x 4/3]
= (15/2 - 3)
= 9 / 2 = 41/2
Let circumference = 100 cm .
Then, ? 2?r = 100
? r = 100/2?
=50/?
? New circumference
= 105 cm
Then, 2?R = 105
? R = 105 / (2?)
&rArr Original area = [ ? x (50/?) x (50/?) ]
= 2500/? cm2
? New Area = [? x (105/2?) x (105/2?)]
= 11025 / (4?) cm2
? Increase in area = [11025/(4?)] - 2500/? cm2
= 1025 / 4? cm2
Required increase percent [1025/(4?)] x 2500/? x 100 = 41/4%
= 10.25%
Clearly, Yogesh beats vijay by 20 s.
Distance covered by vijay in 400 s = 1000 m
[? 6 min 40 s = 400 s]
Distance covered by Vijay in 20 s = (1000/400) x 20 m = 50 m
? Yogesh beats Vijay by 50 m.
1st pipe takes 1 h to fill 1/2 part of the tank.
So, time taken to fill the whole tank (m) = 2 h
2nd pipe takes 1 h to 1/3 part of the tank
So, time taken to fill the whole tank (n) = 3 h
Let 3rd pipe takes P h to empty the tank = x
? 1/m + 1/n - 1/x = 7/12 ? 1/2 + 1/3 - 1/x = 7/12
? 1/x = (6 + 4 - 7)/12 = 3/12 = 1/4
? x = 4 h
(0.96)3 - (0.1)3/ [(0.96)3 + 0.096 + 0.01]
= (0.96)3 - (0.1)3 = (0.96 - 0.1) [(0.96)2 + 0.96 x 0.1 + (0.1)2]
[? a3 - b3 = (a - b) (a2 + ab + b2)]
= (0.96 - 0.1) [(0.96)2 + 0.096 + 0.01]/(0.96)2 + 0.096 + 0.01
= 0.96 - 0.1 = 0.86
Let The required distance be y km.
Then, y/3 + y/2 = 5
? 2y + 3y = 30
? y = 6 km
Given expression
= [(a + b)2 + (a - b)2] / [a2 + b2]
= 2(a2 + b2) / (a2 + b2)
= 2
where, a = 238, b = 131
Speed in m/sec = 36 km/hr x 5/18 = 10m/sec
Distance covered by train in crossing the bridge = Speed of train in m/sec x time in sec = 10 m/sec x 30 sec = 300 m
Now, we know that
Distance covered by train in crossing the bridge= Length of train + Length of bridge
Therefore, Length of bridge = 300m - 200m = 100m
Time taken to fill the whole tank = (12 x 14 x 8) / (14 x 8 + 12 x 8 - 12 x 14) = 168/5 minutes
? In 7 minutes 5/168 x 7 = 5/24 part of the tank will be filled
? Requied answer = 1 - 5/24 = 19/24 part
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