GATE Questions

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Let the avg age of 7 boys be 'p' years
Let the age of the girl be 'q' years
From given data,
The age of 7 boys = 7p years
Now the new average = (p + 1) when 22 yrs is replaced by q
Now the age of all 7 will become = 7(p + 1) yrs
Hence, 7p - 22 + q = 7(p + 1) yrs
7p - 22 + q = 7p + 7
q = 22 + 7 = 29

Therefore, the age of girl = q = 29 years.

Let the the age of the elder boy = E

Let the the age of the younger boy = Y

Given that Y = cube root of EY

=> Y3 = EY => E = Y2 .....(1)
By the condition of number replacement the age of the father is YE

The Mother's age = EY/2

But she is 3 years less than father => EY/2 + 3 = YE
2YE = EY + 6 ......(2)

Then now from the given options we can identify which satisfies the all the conditions.

Here Y =2 and E = 4 satisfies all the conditions.

Natural resources are resources taken from nature to satisfy our needs. As wild animals are on the earth naturally, they are considered as natural resources.

Hence, the given statement is false.

As given Kapil's 8th birthday was celebrated 2 years ago,

Kapil’s present age = 8 + 2 = 10 years.

Father's age is twice of Kapil’s age after 10 years.
=> F + 10 = 2 (K + 10) = 2 (10+ 10)
F = 30years,

Avanthi's age =1/6(F) = 30/6 = 5 years.

Here total parts of milk and water in the solution is 6+2 = 8 parts.

1part = 640/8 = 80

old mixture contains 6parts of milk and 2 parts of water(6:2).

To get new mixture containing half milk and half water, add 4parts of water to the old mixture then 6:(2+4) to make the ratio same.

i.e, 4 x 80 = 320 ml.

N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)

= H.C.F. of 3360, 2240 and 5600 = 1120.

Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4

wine(left)wine(added) = 343169

It means  wine(left)wine(initial amount) = 343512    (since 343 + 169 = 512)

Thus,  343x = 512x1 - 15k3

 343512 = 783 = 1 - 15k3

 1-15k=78=1-18

Thus the initial amount of wine was 120 liters.

60(x + 1) = 64x

X = 15

60 x 16 = 960 km