A five-digit number, which is divisible by 3, is formed when sum of digits is also divisible by 3.
So, combination formed using six-digits, which are divisible by 3
= 5 + 4 + 3 + 2 + 1 = 15
= 5 + 4 + 2 + 1 + 0 = 12
So, set of number are (5, 4, 3, 2, 1) and (5, 4, 2, 1, 0).
Number formed by using 1st set = 5 x 4 x 3 x 2 x 1 = 120
Similarly, using 2nd set = 4 x 4 x 3 x 2 x 1 = 96
Hence, using 2nd set, underlined place cannot be filled by 0, otherwise it will become a four-digit number.
? Total number = 120 + 96 = 216
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
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