Let the smallest of these number be x. The other two numbers are (x + 2) and (x + 4).
=> x + (x + 2) + (x + 4) = (X + (X+2) + (x+4)) / 3 + 44
=> 3x + 3 $\times$ (x + 2) + 3 $\times$ (x + 4) = x + (x + 2) + (x + 4) + 132
=> 9x + 18 = 3x + 138
=> 6x = 120
=> x = 20
Therefore, the largest number is 24.
Total distance = addition of length of the two trains = 140 + 120 = 260 meters
As the two trains are travelling in the same direction, their relative speed is:
=> v = | v1 - v2 | = | 40 - 60 | = 20 km/hr. = 20 $\times$ 1000/60 = 1000/3 meters/min
=> t = 260/ 1000 $\times$ 3
=> t = 0.78 minutes
Let the average weight of the 59 students be A.
So, the total weight of the 59 of them will be 59 $\times$ A.
Given that when the weight of this student who left is added, the total weight of the class = 59A + 45
When this student is also included, the average weight decreases by 0.2 kgs.
So,
=> (59A+45)/60 = A-0.2.
=> 59A + 45 = 60A - 12.
=> 45 + 12 = 60A - 59A.
=> A = 57.
The relative speed of A and B is 6 km/hr. = 1.67 m/s
As the car passes A after 10s, the distance between A and B after 10s (i.e. at 11th second) is the distance covered by car in 1 second.
Therefore, at t = 11, d = 1.67 $\times$ 11
d = 18.33 m
v = d/t = 18.33/1 = 18.33m/s
v = 66 km/hr.
Given,
Principal = Rs. 4000, Amount = Principal + SI = Rs. 4600
SI = Amount - Principal = 4600 - 4000 = Rs. 600
Time = T = 5 years and SI = Rs. 600
Since, SI =PRT/100
=> 600 = 4000 $\times$ R $\times$ 5/100
=> 600 = 200R
=> R = 3 % p.a.
Now the new interest rate is = 3% + 3% = 6 % p.a.
=> SI = PRT/ 100 = 4000 $\times$ 6 $\times$ 5/ 100 = Rs. 1200
Hence the required amount = Principal + SI
= 4000 + 1200 = 5200.
Here the mark obtained by the candidate is 120 and the candidate fails by 78 marks.
Therefore the passing marks is (120+78) = 198
Let the total marks be x. Then,
=> 55/100 $\times$ x = 198
=> x = 360.
Total time taken = (160/64 + 160/80) hrs. = 9/2 hrs.
$\therefore$ Average speed = (320 x 2/9) km/hr. = 71.11 km/hr.
As Shyam is helped by Ram and Singhal every third day, Shyam works for 3 days while Ram and Singhal work for 1 day in every 3 days.
Therefore, the amount of work done in 3 days by Shyam, Ram and Singhal:
=> 3/20 + 1/30 + 1/60
=> 1/5 of the job.
Hence, it will take them 5 times the amount of time = 3 $\times$ 5 = 15 days.
Let CP of each kg. of sugar = Rs.1.
Cost Price of 200 kg of sugar = Rs.200.
Let quantity of sugar sold with 25% profit be X.
Therefore, (200 - X) kg of sugar sold at a profit of 10%
Then,
=> (125/100 $\times$ X) + 110/100 (200 - X) = 115/100 $\times$ 200
=> 125X + 110(200 - X) = 115 $\times$ 200
=> 125X + 22000 - 110X = 23000
=> 125X - 110X = 23000 - 22000
=> 15X = 1000
=> X = 1000/15
=> X = 66.66 kg =67(approx.)
Let amount subscribed for R be x.
Therefore, Q = x + 5000 and P = x + 5000 + 4000 = x + 9000
So, x + x + 5000 + x + 9000 = 50000
=> 3x = 36000
=> x = 12000
=> P: Q: R = 21000: 17000: 12000 = 21: 17: 12
Hence, P`s share = 25000 X (21/50) = Rs. 10,500.
Let Nehas present age be x years.
Her age 12 years ago = (x - 12) years
Therefore, her mothers age 12 years ago = 4(x - 12)
Her mothers present age = 4x - 48 + 12 = 4x - 36
Nehas age after 12 years = x + 12
Her mothers age after 12 years = 4x - 36 + 12 = 4x - 24
=> 4x - 24 = 2(x + 12)
=> 4x - 2x = 24 + 24
=> x = 24
Therefore, Nehas present age = 24
Hence, Her mothers present age = 4x - 36 = 4(24) - 36 = 60 years.
Let the speed of the trains be x and y respectively
length of train1 = 27x
length of train2 = 17y
Relative speed= x + y
Time taken to cross each other = 23 s
=> (27x + 17 y)/(x+y) = 23
=> (27x + 17 y)/ = 23(x+y)
=> 4x = 6y
=> x/y = 6/4 = 3/2.
It is time, we looked at the latent causes. Where does the strength of India lie? Not in numbers, not necessarily in our moral stands on international issues. In modern times, the strength of a nation lies in its achievements in science and technology. This is not to say that other fields do not count.
In the five decades after independence, we have yet to demonstrate our originality in applied science and technology. Though Japan also started like us, yet by cultivating the technology of the West, the Japanese adapted, improved and displayed originality in several areas of science and technology. The generationwhich is at the helm of affairs in science and in our country after independence mostly consisted of self-seekers. By and large with a few exceptions. The science and technology managers in India concentrated in gaining power and influence.
They loved publicity. Most of them stopped doing science while they managed science. Things would have been better had they been humble enough to acknowledge the difference between doing and managing science. Instead they claimed they were the foremost in science and technology, simply because theywere at the helm of affairs. As a result, they ceased to inspire the younger lot. India continues to be a borrower of science and technology, even though its potential for originality is substantial.
Our achievements in nuclear science and technology may be dazzling to our people. But, in worth and originality, they are ordinary and routine. While our own people remain ignorant the people of other countries know all about the pretensions to knowledge of our nuclear science and technology managers. Our subtle way of sabotaging our nuclear goals is to help hollow persons reach and remain at the helm of affairs. International bodies come in as handy tools in that subtle process. The veil of secrecy effectively protects the mismanagement in our nuclear establishments. The talk of national security comes as an easy weapon to prevent any probe into mismanagement. On nuclear matters the media in our country, by and large avoid the mismatch between promise and hence performance in the nuclear field does not get exposed as much as the mismanagement in other fields.
What does the author mean by `doing` science?Replace `the citys jail` with `the city jail`.
His over-enthusiasm has now been ________ because of his ________ to mobilize the required support.
Anything in this shop can be bought, ________
(X) It is a general tendency among human beings that as our familiarity with a person increases, our aversion towards him too starts going higher.
(1) when the relationship grows deeper, it brings the shortcomings and deficiencies of a person to the fore front.
(2) As the relationship starts, the good qualities of a person come into notice and these attract the other towards him and his other qualities of lesser grade remain in the rear.
(3) The real qualities of a person are observed only when relationship with him becomes closer and go to the level of intimacy.
(4) No person on this earth can claim himself or herself to be free from defects and shortcomings.
(Y) A person by nature brings forth his better instincts and traits to show to others and tends to hide his weak points and shortcomings.