How many seconds will a 500 metre long train take to cross a man walking with a speed of 3km/hr in the direction of the moving train if the speed of the train is 63km/hr?

Let the present age of Rani be R. Now, 2R/3 + 12 = R + 3 or, R - 2R/3 = 12 - 3 or, R/3 = 9 or, R = 27 years

1 + 8 = 9 9 + 8 = 17 17 + 8 = 25 25 + 8 = 33 33 + 8 = 41

4 × 2 + 1 = 9 9 × 2 - 1 = 17 17 × 2 + 1 = 35 35 × 2 - 1 = 69

Area of triangle = 1/2 × base × height = 1/2 × 8 × 12 = 48 cm2

Weight of 1/2 glass of milk = 1 - 3/4 = 1/4 kg So, weight of full glass of milk = 2 × 1/4 = 1/2 kg So, weight of the glass = 1 - 1/2 = 1/2 kg = 0.5 kg

Here, 2 year 6 months = 2.5 years Principal with simple interest, A = P( 1 + n r) Now, 504 = 450( 1 + 3 × r) or,  1 + 3r = 504/450 or, 3r = 504/450 - 1 or, 3r = (504 - 450) / 450 or, 3r = 54 / 450 or, r = 54 / (450 × 3) or, r = 1/25 Again,  A = 650( 1 + 2.5 × 1/25) or, A = 650 × (25 + 2.5)/25 or, A = 650 × 27.5 / 25 So, A = 715 Rs.

Let the total profit be P. Now, A's share of profit, 4 / (4 + 7 + 8) × P = 16000 or, 4P/19 = 16000 or, P = 16000 × 19 / 4 = 76000 Rs.

Let they receive A, B & C Rs. respectively. Now, A = (B + C) / 2 or,  2A = B + C - - - - - - - - - - (i) Again, B = (A + C) / 4 or, 4B = (A + C) or, 4B = (B + C) / 2 + C or, 4B = B/2 + C/2 + C or, 4B - B/2 = 3C/2 or, 7B/2 = 3C/2 or, B = 3C/7 - - - - - - - (ii) Now, 2A = 3C/7 + C  [from (i)] or, 2A = 10C/7 or, A = 5C/7 - - - - - - (iii) From (ii) and (iii),  B : C = 3 : 7 C : A = 7 : 5 So,  A : B : C = 5 : 3 : 7 A will receive = 5 / (5 + 3 + 7) × 5625 =  1875 Rs. B will receive = 3 / (5 + 3 + 7) × 5625 =  1125 Rs. C will receive = 7 / (5 + 3 + 7) × 5625 =  2625 Rs.

Let the cost price and sell price be A and S respectively. ATQ,   (A - 2S/3) /A = 20/100 or,  (A - 2S/3) / A = 1/5 or, (A - 2S/3) = A/5 or, 2S/3 = A - A/5 or, 2S/3 = 4A/5 or, S = 4A/5 × 3/2 or, S = 6A/5 Now, profit = (S - A) / A × 100%   = (6A/5 - A) / A × 100% = (A/5) / A × 100% =  20%