GATE Questions

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Ratio of times taken by P & Q = 100 : 130 = 10:13

Let Q takes x days to do the work

Then, 10:13 :: 23:x

=> x = 23x13/10

=> x = 299/10

P's 1 day's work = 1/23

Q's 1 day's work = 10/299

(P+Q)'s 1 day's work = (1/23 + 10/299) = 23/299 = 1/13

Hence, P & Q together can complete the work in 13 days.

Let the present ages of Ajay and Vijay be 'A' and 'V' years respectively.

=> A - 8 = 4/3 (V - 8) and A + 8 = 6/5 (V + 8)

=> 3/4(A - 8) = V - 8 and 5/6(A + 8) = V + 8

V = 3/4 (A - 8) + 8 = 5/6 (A + 8) - 8

=> 3/4 A - 6 + 8 = 5/6 A + 20/3 - 8

=> 10 - 20/3 = 10/12 A - 9/12 A

=> 10/3 = A/12 => A = 40.

a and b give, profit after 3 years = Rs.(3/8 x 22000) = Rs.8250.

From c also, profit after 3 years = Rs. (2750 x 3) = Rs. 8250.

∴ P's share = Rs.(8250 x 5/11) = Rs. 3750.

Thus, (either C is redundant) or (a and b are redundant).

Present total age of the members = 26(5) = 130 years.

Present age of the youngest member = 10 years

Present total age of the remaining four members = 130 -10 = 120 years

Their average age at the time of the birth of the youngest member = 120-4×104 = 30 - 10 = 20 years.

Speed in upstream = Distance / Time = 3 x 60/20 = 9 km/hr.

Speed in downstream = 3 x 60/18 = 10 km/hr

Rate of current = (10-9)/2 = 1/2 km/hr.

65292

1st digit is 3 x 2 = 6

3rd digit is 5-3 = 2

4th digit is 5+4 = 9 

6+5 = 2+9 = 9+2 = 11

The Kharoshi script is an ancient script used by the ancient Gandhara culture of South Asia primarily in modern-day Afghanistan and Pakistan to write the Gandhari language (a dialect of Prakrit) and the Sanskrit language.