A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:

Given in the question,
Price of 6 toys is Rs. 264.37.
? Price of 1 toys is Rs. 264.37/ 6 .
? Price of 5 toys is Rs. 264.37 x 5 / 6 .
? Price of 5 toys is Rs. 44 x 5 .
? Price of 5 toys is Rs. 220.

Ratio of the speeds of A and B = 5 : 3
Thus, in a race of 5m, A gains 2 m over B.
2 m are gained by A in a race of 5 m.
40 m will be gained by A in a race of (5/2) x 40 m = 100 m
? Winning post is 100 m away from the starting point.

Velocity of stream = (downstream velocity - upstream velocity)/2
= (60/10 - 60/30)/2
= 2 km/hr

Let their ages one years ago be 4x and 3x years.
? (4x + 2)/(3x + 2) = 5 / 4
? 4(4x + 2) = 5(3x + 2)
? x = 2
? Sum of their present ages = (4x + 1) + (3x + 1) = 16 years

Required number
= 786 x 964 = 757704

Let the C.P. be Rs. x
Then 2(69 - x) / 100 = (78 - x) / 100
? 138 - 2x = 78 - x
? x = 60
? C.P. = Rs. 60

Score of A = 100 points
Score of B = 65 points
? A can give (100 - 65 ) = 35 points to B.

Given expression = log 8 + log (1/8)
= log 8 x (1/8)
= log 1
= 0

Let N = 3¹² x 2⁸
? log N = 12 x log3 + 8 x log 2
? log N = 12 x 0.47712 + 8 x 0.30103
? log N = 8.13368
? No.of digits = 8 + 1 = 9

Place value of 5 in 65231 = 5 x 1000
= 5000

Face value = 5

required product = 5000 x 5 = 25000