Let length of tunnel is x meter.
Distance = 800 + x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr. = 78 $\times$ 5/18 m/s = 65/3 m/s
Distance = Speed $\times$ Time
=> 800 + x = 65/3 $\times$ 60
=> 800 + x = 20 $\times$ 65=1300
=> x = 1300 - 800 = 500.
Let the age of younger person is x,
Then elder person age is (x+16)
=> 3(x-6) = (x+16-6) [6 years before]
=> 3x-18 = x+10
=> x = 14.
So other person age is x + 16 = 30.
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
Quantity of milk = 90 $\times$ 2/3 = 60 liters.
Quantity of water in it = (90 - 60) = 30 liters.
New ratio required = 2: 3.
Let the quantity of water to be added further be x liters.
Then, milk: water = 60/(30+x) = 2 : 3 => 180 = 60+ 2x => x = 60.
$\therefore$ Quantity of water to be further added is 60 liters.
Time taken by A to complete the work = 15 days
Time taken by B to complete the work = 10 days
Work done by A in a day = 1/15
Work done by B in a day = 1/10
Work done by A and B together in a day = 1/15 + 1/10 = 1/6
So work done by A and B together in a two days = 1/3
Work remaining when B leaves = 1 - 1/3 = 2/3
Now, A alone completes the remaining 2/3 work
Time taken by A to complete 2/3 work = 2/3 $\times$ 15 = 10 days.
So total time taken to complete the work = (2+ 10) days = 12 days.
Let Abhays speed be x km/hr.
Then, 30/x - 30/2x = 3
=> 6x = 30
=> x = 5 km/hr.
Let, S = sample space, E = event of selecting 1 girl and 2 boys.
Then, n(S) = Number of ways of selecting 3 students out of 25 = 25C3 = 2300.
n(E) = 10C1 x 15C2 = 1050.
P(E) = n(E)/n(s) = 1050/2300 = 21/46.
Work done by X in 4 days = (1/20 - 4) = 1/5
Remaining work = 1 - 1/5 = 4/5
(X+Y)`s 1 day`s work = 1/20 + 1/12 = 8/60 = 2/15
Now, 2/15 work is done by X and Y in 1 day.
So, 4/5 work will be done by X and Y in (15/2 x 4/5) = 6 days.
Hence, total time taken = (6 + 4) days = 10 days.
Let the quantity of the wine in the cask originally be x liters.
Then, quantity of wine left in cask after 4 operations = $[x(1-(8/x) ^4] $liters.
=> $[x(1-(8/x) ^4]$/x = 16/81
=>$ (1-8/x) ^4$ = $(2/3) ^2 $
=> (x - 8)/x = 2/3
=> 3x - 24 = 2x
=> x = 24.
Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
=> (140/100 $\times$ 5x), (150/100 $\times$ 7x) and (175/100 $\times$ 8x)
=> 7x, 21/2x and 14x.
The required ratio = 7x : 21x/2 : 14x.
=> 14x : 21x : 28x
=> 2 : 3 : 4.
The reward was not commensurate __________ work done by us.
Of the (1)/ two cars that you (2)/ have, the new Maruti is without (3)/ any question, the cheapest (4)/ to run.
S1: A gentleman who lived alone always had two plates placed on the table at dinner time.
P: One day just as he sat down to dine, the cat rushed in to the room.
Q: One plate was for himself and other was for his cat.
R: she drooped a mouse into her own plate and another into her master plate.
S: He used to give the cat a piece of meat from his own plate.
S6: In this way the cat showed her gratitude to her master.
Theodore Roosevelt was born with asthma and poor eyesight, yet this sickly child later won fame as a political leader, a Rough Rider, and a hero of the common people. To conquer his handicaps, Teddy trained in a gym and became a lightweight boxer at Harvard. Out west, he hunted buffalo and ran a cattle ranch. Back east, he became a civil service reformer and police commissioner. He became President McKinley`s assistant Navy secretary during the Spanish-American War. Also, he led a charge of cavalry Rough Riders up San Juan Hill in Cuba. After achieving fame, he became governor of New York and went on to become the vice president.When McKinley was assassinated, Theodore Roosevelt became the youngest president at age 42. He is famous for his motto, Speak softly and carry a big stick. Roosevelt battled for meat inspection and pure-food laws. Also, he wanted to save the forests and break the grip that big business had on steel and oil. Roosevelt persuaded the diplomats of warring Russia and Japan to make peace.
Which of the following states the main idea of the passage?