CAT Questions

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1/15 + 1/12 + 1/R = 1/6, we got R = 60 (it means R will take 60 days to complete the work alone)

so ratio of work done by P:Q:R = 1/15 : 1/12 : 1/60 = 5 : 4 : 1

so R share = (1/10) x 1200 = 120.

Let the total Profit be Z.
Ramu's profit share is 2/3 of profit (i.e 2Z/3)
Ravi's profit is (Z-2Z/3) =Z/3
Hence the profit ratio is , Ravi : Ramu = Z/3 : 2Z/3 = 1:2

Let total Capital be Rs.X and Ramu has contributed for Y months.Since Ramu's profit share is 2/3, his invest share will be 2/3 in capital.

Ravi's invest for 16 months / Ramu's invest for Y months = Ravi's profit share / Ramu's profit share
i.e. (X/6 x 16) / (2X/3 x Y) = 1/2

Solving the above equation, we get Y = 8.
So Ramu's money has been used for 8 months.

Fatehpur Sikri in Uttar Pradesh.

The given statement implies that 64 Squares on Carrom Board.

The molar mass of H2O can be calculated as the following.

M(H2O)= [2 x M(H)] + [M(O)].

And we know that M(H) = 1g/mol, M(O) = 16g/mol.

So, M(H2O)= 2x1 + 16 = 18g/mol,

That means 1 mole of H2O contains 18g.

Hence, one mole of H2O corresponds to 18 grams.

We need to find the total cost to send r messsages, r > 1000.

The first 1000 messsages will cost Rs.p each (Or) 

The total cost of first 1000 messsages = Rs.1000p

The remaining (r - 1000) messsages will cost Rs.q each (Or)

The cost of the (r - 1000) = Rs.(r - 1000)y

Therefore, total cost = 1000p + rq - 1000q

= 1000(p - q) + qr

An object at rest may have Potential energy.

Required probability is given by P(E) = n(E)n(S) = 14C2 = 16