GATE Questions

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Walking at 3/4th of usual rate implies that time taken would be 4/3th of the usual time. In other words, the time taken is 1/3rd more than his usual time

so 1/3rd of the usual time = 15min
or usual time = 3 x 15 = 45min = 45/60 hrs = 3/4 hrs.

Cost price of the article is given by

= 400x100/(20+20)

= Rs.1000

India is a land of rivers. Rivers are generally treated as mothers and almost every major river of India has a legend regarding its origin.

The Ganges or Ganga is the longest river of India, if we consider the total distance covered by a river within India. Two major rivers of the Indian subcontinent – Brahmaputra and Indus – are though longer than the Ganges, but the distances these two rivers cover within India are much shorter than that of the Ganges.

The Ganges is the most sacred river to the Hindus. The Ganges originates from Gangotri Glacier (Uttarakhand). The total length that the Ganges covers during its journey is 2,525 kilometers (1569 miles) before it discharges in the Bay of Bengal.

The Godavari, also known as 'Dakshin Ganga' – the South Ganges, is the second longest river of India. It originates from Triambakeshwar, Nasik (Maharashtra), and travels through Chhattisgarh, Telangana and Andhra Pradesh, before discharging into Bay of Bengal.

Given,
Compound rate, R = 10% per annum
Time = 2 years
C.I = Rs. 420
Let P be the required principal.
A = (P+C.I)
Amount, A = P1 + r100n

(P+C.I) = P1 + 101002

(P+420) = P[11/10][11/10]

P-1.21P = -420

0.21P = 420

Hence, P = 420/0.21 = Rs. 2000

Days in 4 years => 

Let the first year is Normal year i.e, its not Leap year. A Leap Years occurs once for every 4 years.

4 years => 365 + 365 + 365 + 366(Leap year)

4 years => 730 + 731 = 1461

Therefore, Number of Days in 4 Years = 1461 Days.

Birds speeds in mtrs/sec is 'x' and '2x' .
While flying from Engine to end, relative speed = (x+10) m/sec
from end to engine, flying speed = (2x - 10) mtr/sec
so
1000/(x+10) + 1000/(2x-10) = 187.5 secs
solving it, we get
so x = 8.728 m/sec and 2x= 17.456 m/sec

x = 31.4208 km/hr and 2x = 62.8416 km/hr.

P = Rs. 900, R = 3 ½ % = 7/2 %, T = 2 years. 

Therefore, 

S.I. = PTR/100

S.I. = Rs. (900 x 7/2 x 2/100) = Rs. 63

Now, P = Rs. 200, S.I. = Rs. 63, R = 5 %

Time = ((100 x 63) / (200 x 5) ) years = 6.3 years.

Let the cost price be Rs. 100
Then, market price is Rs. 140
Now, the first discount is of 28.57% Rs.140 =~ Rs. 40
Hence, its selling price = 140 - 40 = Rs. 100
Now since Rana is selling at cost price, any further discount will be equal to loss percentage.
The next dicount of 12.5% will be the loss percentage to Rana.