GATE Questions

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One-quarter of one-seventh = 1/4 x 1/7
= 1/28
Now, 1/28 of a land costs = Rs. 30,000
Thus, 8/35 of the land will cost = 30,000 x 28 x 4/15
= Rs. 2,24,000.

343 = 73,  1331 = 113 , 2197 = 133, 121 = 112

343, 1331, 2197 are perfect cubes, but not 121.

Given that Rs. 1860 will become Rs. 2641.20 at 12%

=> Simple Interest = 2641.20 - 1860 = Rs. 781.20

We know I = PTR/100

=> 781.20 x 100 = 1860 x T x 12

=> T = 78120/1860x12

=> T = 78120/22320

=> T = 3.5 years.

Given S = 17 yrs

A = 16 yrs

B = 12 yrs

Average = 17 + 16 + 12/3 = 15 yrs

Given if Aslam added to them, their average increases by 5

=> Average of 4 members = 20

Let the age of Aslam be 'x'

Then, 

17 + 16 + 12 + x /4 = 20

=> x = 80 - 45

=> x = 35. 

Hence, the age of Aslam is 35 yrs.

(16M + 12W) x 20 = 18W x 40

=> 2M = 3W

Then,
Convert all men into women

12M + 27W = 27 + 12 x 3/2W = 45W

Let number of days required be 'D'

=> 18 x 40 = 45 x D

=> D = 16 days.

Total coins 30

In that,

1 rupee coins 20

50 paise coins 10

Probability of total 1 rupee coins =  20C11

Probability that 11 coins are picked = 30C11

Required probability of a coin now picked from the box is 1 rupee = 20C11/30C11 = 2/3.

Say total cost price of tea is x.
Then total profit at a rate of 15% is = (15x/100)
According to question,
15x/100 = 60
so x = 400
C.p of the tea is Rs. 400.
so total selling price will be = (400+60) = Rs.460
so the quantity of the tea will be = (460/5.75) = 80kg.

Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8.

Seats for Mathematics, Physics and Biology in a school are 5x, 7x and 8x.

There is a proposal to increase these seats by 40%, 50% and 75% respectively.

Then Seats for Mathematics, Physics and Biology in a school will be

1.4 X 5x, 1.5 X 7x and 1.75 X 8x and

ratio will be 7 : 10.5 : 14  => 2:3:4.