T9 = a + (9 - 1)d = a + 8d
T5 = a + (5 - 1)d = a + 4d
T9 - T5 = 32
? (a + 8d) - (a + 4d) = 32
? 4d = 32
? d = 8
T9 + T5 = (a + 8d) + (a + 4d)
= 2a + 12d
T9 + T5 = 114
? 114 = 2(a + 6d)
? a + 6d = 57
? T8 = a + 7d
= a + 6d + d
= 57 + 8 = 65
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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