GATE Questions

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The sum of the digits in 708, 618 and 816 is 15, but not in 392.

Yes, footsteps are what we take more, the more we leave behind. 

Let us assume S as number of shirts and T as number of trousers
Given that each trouser cost = Rs.70 and that of shirt = Rs.30
Therefore, 70 T + 30 S = 810
=> 7T + 3S = 81......(1)
T = ( 81 - 3S )/7

We need to find the least value of S which will make (81 - 3S) divisible by 7 to get maximum value of T
Simplifying by taking 3 as common factor i.e, 3(27-S) / 7
In the above equation least value of S as 6 so that 27- 3S becomes divisible by 7

Hence T = (81-3xS)/7 = (81-3x6)/7 = 63/7 = 9

Hence for S, put T in eq(1), we get
S = 81-7(9)/3 = 81-63 / 3 = 18/3 = 6.
The ratio of T:S = 9:6 = 3:2.

Alloy of copper and zinc is called as Brass.

In vulcanization, cruder rubber is heated with 3% sulphur at about for 1200C for 2-3 hours.

Vulcanised rubber is a vastly improved product.

As now, the time 4 : 48 pm after 45 min it will be

4:48 + 45 min = (4 hrs : 48 + 12 min) pm + 33 min = 5 hrs : 33 min pm.

Hence, it is 5:33 pm.

An ignition safety switch is a safety device can shut off the engine if the operator falls off the PWC or out of the powerboat, or is otherwise thrown from the proper operating position.

How it works:

It allows the engine of the vehicle to shut off or to be turned off immediately as it is to prevent further complications to happen as this is being used when an emergency is launched

Where it is used:

Most powerboats and PWCs come equipped by the manufacturer with an emergency engine cut-off switch.

Let the age of sushma be x and
the age of her son is y
Then five years before x-5=5(y-5) ...(1)
Five years hence x+5 = 3(y+5)-8 .....(2)

By soving (1) & (2), we get
5y - 15 = 3y + 7
y = 11 => x = 35

Therefore, the age of Sushma = 35 and her son = 11.