GATE Questions

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Profit ratio X & Y = (700 × 3) + (700 × 5/7× 3) + (700× 5/7 + 200 × 3/5 )× 6 : 600 ×12
X:Y= 7320 : 7200= 183:180
∴ X’s share from profit = 183 × 726/(183+180) = Rs. 366.

Let the cost price of the fruits be 'C.P'

From the given data, after analysis it can be solved as

(121% of C.P) - (125% of 91% of C.P) = 29

$$\begin{gathered} 121100 C.P - 125100 x 91100 x C.P = 29 \\ 121100 - 125 x 91100 x 100 C.P = 29 \\ (12100 - 125 x 91) C.P = 290000 \\ (12100 - 11375) C.P = 290000 \\ 725 C.P = 290000 \\ C.P = 400 \end{gathered}$$

Hence, the cost price of the fruits = Rs. 400.

The Apex body for The national sport Hockey India pitched Jharkhand's Samurai Tete, former Team India skipper, for the Dhyan Chand Lifetime Achievement Award 2016.

Sumrai Tete is a member of the India women's national field hockey team. She played with the team when it won the Gold at the Manchester 2002 Commonwealth Games.

Probability of not hitting the ball = 1- 1/4 =
Then, the probability that the batsman will hit the ball =

Quarter of Kg means 250 gm

Less weight, less price (Direct Proportion)

So,

250 : 200 :: 60 : x => x = 48

So 200 gm will cost 48 paise.

Let the place be at a distance of 'd' kms

From the given data,

$$\begin{gathered} d5 - 1 + d5 + 1 = 7560 kms \\ d4 + d6 = 54 \\ \end{gathered}$$

5d/12 = 5/4 => d = 3 kms.

Hence, the place is 3 kms far.

In a family with 2 children there are four possibilities:
1) the first child is a boy and the second child is a boy (bb)
2) the first child is a boy and the second child is a girl (bg)
3) the first child is a girl and the second child is a boy (gb)
4) the first child is a girl and the second child is a girl (gg)

But already given that one child is boy. So we have three possibilities of (bb)(bg)(gb).
n(E)= both are boys=BB=1
n(S)= 3
Required probability P = n(E)/n(S) = 1/3.