GATE Questions

---

Let the sum be Rs. P
P{ 1+81002- 1 } = 2828.80

It is in the form of  a2-b2 = a+ba-b

P(8/100)(2 + 8/100) = 2828.80

P = 2828.80 / (0.08)(2.08)

= 1360/0.08 = 17000

Principal + Interest = Rs. 19828.80

Let Shilpa's present age is p years

According to question,

p = 4(x+4) – 4(x–4)

p = 4x+16 – 4x+16

p = 32

Shilpa's present age = 32 years

Rajeev is four years older than Shilpa

=> Shilpa's present age = Rajeev's age 4 years before.

=> Rajeev's age 4 years before = 32 years.

Let present Anirudh's age be 'A' and Bhavana's age be 'B'

Given seven years, their ratio is 7:9

=> A-7 : B-7 = 7 : 9

=> 9A - 7B = 14 .......(1)

And given,

Chandhu is 12 years older than A nad 12 years younger than B

=> C = A + 12....(2)

=> B = C + 12

=> B = A + 12 + 12 .....(From (2))

=> B = A + 24 ....(3)

Put (3) in (1)

9A - 7(A+24) = 14

9A - 7A - 168 = 14

2A = 182

=> A = 91 years

=> C = A + 12 = 91 +12 = 103 years.

Using pythagarous theorem,
distance travelled by first train = 36x5/18x30 = 300m
distance travelled by second train = 48x5/18x30 = 400m
so distance between them =√( 90000 + 160000) = √250000 = 500mts.

One fathom = 1.8288 meters = 6 feet

A fathom is a unit of length used especially for measuring the depth of water.

= log tan10+log tan890 + log tan20+ log tan880+⋯⋯+log tan450  

= log [tan10 × tan890] + log [tan20 × tan880 ] +⋯⋯+log1  

∵ tan(90-θ)=cotθ and tan 450=1  

= log 1 + log 1 +.....+log 1 

= 0.

% Profit with respect to A = 40 + 50 + (40 x 50)/100 = 90 + 20 = 110 %.