GATE Questions

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Let the present age of Pinky be x years

Then the age of Mary is x - 12 years

After 3 years,

Ratio of  MaryPinky = x - 9x + 3 = 58

8x - 72 = 5x +15

=> 3x = 87

=> x = 29

=> Age of Pinky = 29 years

=> Age of Mary = 29 - 12 = 17 years

Present age of Sam = 29 + 17 = 46

Before 15 years Sam age = 46 - 15 = 31 years.

For 1 hour, 20 minutes is slower, then for
06 miuntes - 2 minutes is slower
30 minutes - 10 minutes
Actual time | false time
12 12
01 PM 12:40 PM (20 minutes slower)
02 PM 01:20 PM
03 PM 02:00 PM

So, when actual time is 3pm, the false time is 2 pm.
So, it loses 60 minutes when it shows 2 pm.

K = 100 L = 130
130------ 30
100------- ? => 23 1/13 %

Let Rs. K invested in each scheme

Two years C.I on 20% = 20 + 20 + 20x20/100 = 44%

Two years C.I on 15% = 15 + 15 + 15x15/100 = 32.25%

Now,

(P x 44/100) - (P x 32.25/100) = 528.75

=> 11.75 P = 52875

=> P = Rs. 4500

Hence, total invested money = P + P = 4500 + 4500 = Rs. 9000.

Let Mohan present age = p

ATQ,

5/6 x p = p - 5

p = 30

His wifes age = 30 - 3 = 27 yrs.

Boxing is played in the ring whereas Wrestling is played in Arena.

As these three strategies P, Q and R are independent so these will cut cost one after the other.
If initial cost is Rs 100, then
20% cost is cut after initializing strategy P, then cost will remain 80% = 80
further 30% cost is cut after strategy Q, then cost will remain 70% of 80 = 56
further 10% cost is cut after strategy R, then cost will remain 90% of 56 = 50.4

Thus final cost remains 50.4 % of the original cost. Hence net saving is 100 - 50.4 = 49.6 %.

Given that train K crosses a pole in 30 seconds and train L crosses the same pole in one minute and 15 seconds.

Let the length of train K be Lk and that of train L be Ll

given that Lk = 3/4 Ll

As the train K and L crosses the pole in 30 seconds and 80 seconds respectively,
=> Speed of train K = sk = Lk/30

Speed of train L = sl = Ll/80

Lk = 3/4 Ll
=> sk = 3/4 Ll/(30) = Ll/40

Ratio of their speeds = sk : sl
= Ll/40 : Ll/80

=> 1/40 : 1/80  =  2 : 1