GATE Questions

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Suppose A, B and C take x, x/2 and x/3 respectively to finish the work. 

Then, (1/x + 2/x + 3/x) = 1/2 

=> 6/x = 1/2      => x = 12 

So, B takes 6 hours to finish the work.

Let present Anirudh's age be 'A' and Bhavana's age be 'B'

Given seven years, their ratio is 7:9

=> A-7 : B-7 = 7 : 9

=> 9A - 7B = 14 .......(1)

And given,

Chandhu is 12 years older than A nad 12 years younger than B

=> C = A + 12....(2)

=> B = C + 12

=> B = A + 12 + 12 .....(From (2))

=> B = A + 24 ....(3)

Put (3) in (1)

9A - 7(A+24) = 14

9A - 7A - 168 = 14

2A = 182

=> A = 91 years

=> C = A + 12 = 91 +12 = 103 years.

Using pythagarous theorem,
distance travelled by first train = 36x5/18x30 = 300m
distance travelled by second train = 48x5/18x30 = 400m
so distance between them =√( 90000 + 160000) = √250000 = 500mts.

1/2 as a percentage means

1/2 = 0.5 in decimal

Now, in percentage means 0.5 x 100% = 50%.

As given, we have:

Susmitha > Laxmi > Ramya; Ramya = Hema, Ramya > Avanthi

Thus the sequence of heights becomes:

Susmitha > Laxmi > Ramya = Hema > Avanthi

Clearly, Hema is shorter than Laxmi.

Thus, the derivative of sinx by first principle is cosx.

% Profit with respect to A = 40 + 50 + (40 x 50)/100 = 90 + 20 = 110 %.

Let the Original capital amount be Rs. P

Given after 2 years the amount is Rs. 10000

Rate of interest = 30%

According to the question,

$$\begin{gathered} P x 130100 x 130100 = 10000 \\ => P = 1000000169 = 5917 \end{gathered}$$

Therefore, the capital amount P = Rs. 5917