A speaks truth in 60% of the cases and B in 80% of the cases. In what percentage of cases are they likely to contradict each other, narrating the same incident?

Let length of rectangle = 5k
and breadth of rectangle = 3k

According to the quecation,
5k - 3k = 8
? 2k =8
? k = 4
? Lenght = 5k = 5 x 4 = 20 m
Breadth = 3k = 3 x 4 = 12 m

? Required area = Lenght x Breadth
= 20 x 12 = 240 sq m

Let the amount of bill be Rs. 100
Money deducted = Rs. 4
Money receive by holder of the bill = Rs. (100 - 4) = Rs. 96
S.I. on Rs. 96 for 10 months = Rs. 4
Rate = [(100 x 4 x 6) / (96 x 5)] = 5%

Give that A = ? 13800 , R = 5%
T = 5 yr and BG = ?
According to the formula,
BG = [A(R x T)²] / [100(100 + R x T)]
= [13800(5 x 5)²] / [100(100 + 5 x 5)]
= (13800 x 625) / (100 x 125)
= ? 690

Given that, R = 24%, T = 24 months= 2 yr and TD = ? 144
BD = TD + BG
According to the formula,
BG = (TD x R x T)/100 = (144 x 24 x 2)/100
= ? 69.12
? BD = 144 + 69.12 = ? 213.12

A : B = 160 : 150, A : C =160 : 130
B/C = (B/A) x (A/C) = (150/160) x (160/130) = 15/13 = 60 : 52
? In a game of 60, B can give C = (60 - 52)= 8 points

Given in the question,
Face Value = 2520;
Time = 6 months = 1/2 year
Rate of interest = 10 %
As we know the formula,
True Discount = Face Value x ( Rate of Interest x Time in years ) / ( 100 + Rate of interest x Time )
? True Discount = 2520 x (10 x 1/2 ) / (100 + (10 x 1/2 ))
? True Discount = 2520 x ( 5 ) / (100 + ( 5 ))
? True Discount = 2520 x 5 /105
? True Discount = 2520 / 21
? True Discount = Rs. 120

According to the formula,
Time taken by the winner/Distance covered by the loser = Difference of winning time/ Difference of winning distance
? Time taken by P//(1000 - 72) = 12/72
? Time taken by P = (12/72) x 928
= 464/3 = 154²/₃ s

T.D. = (B.G x 100) / (R x T)
= (1 x 100) / (5 x 1)
= ? 20

P.W. = Rs. 1860 - Rs. 60 = Rs. 1800
? B.G. = (T.D.)²/P.W. = (60 x 60)/1800 = Rs. 2