Akshar remembers that the match is after 26th April but before 30th April, while Suresh remembers that the match is after 22nd April but before 28th April. On which date of April is the match?

L.C.M. of 252, 308 and 198 = 2772 seconds
= 46 × 60 + 12 = 46 min 12 seconds.
.

Solving the question by taking two odd numbers greater than 1 i.e. 3 and 5,
for n =3, n( n² -1 ) = 3( 9 - 1) = 24
for n = 5 n( n² -1 ) = 5( 25 - 1) = 120

Using option we find that both the number are divisible by 24.

From the question it is clear that speed of B = 15 / 5 = 3 m/s
The time taken by B to cover 300 m = 300 / 3 = 100 sec.
Hence, time taken by A to complete the race = 100 ? 5 = 95 sec.

Time from 10 a.m on a day to 3 a.m on 4th day = 24 x 3 + 17 = 89 hours.
Now 23 hrs 44 min. of this clock = 24 hours of correct clock.
89 hrs of faulty clock = (24 x 15/356 x 89) hrs = 90 hrs.
So, the correct time is 11 p.m

Let length of the train be x m.
Relative length of the train = (x + 600) m
According to the question,
(x + 600)/30 = 30
? x + 600 = 900
? x = 900 - 600 = 300 m

Let S be the sample space and E be the event of drawing 3 balls out of which 2 are blue and 1 is back .

Then, n (S)= Number of ways of drawing 3 balls out of 9=⁹c₃
= (9 x 8 x 7) / (3 x 2 x 1)
= 84 and

n(E) = Number of ways of drawing 2 balls out of 5 and 1 ball out of 4 .
= ⁵C₂ ⁴C₁₁
= (5 x 4) / (2 x 1) + 4 = 14

? P(E) = n(E)/n(S) = 14/84 = 1/6

We know that, the distance covered by a train in passing a pole or a standing man or a signal post or any other object (of negligible length) is equal to the length of the train.

In this case, train covers 90 m to cross a standing man.
? Length of the train = 90 m

Let quotient = Q and remainder = R
Then, Divisor = 12 Q =5 R
Now, R = 48
? 12Q = 5 x 48
? Q = 20

Dividend = Divisor x Quotient + Remainder
? dividend = ( 20 x 240 + 48 )
= 4848

Factors of composite number = (P₁ +1)(P₂+1)(P₃+1)......(P_n+1).
Where P₁,P₂,P₃... P_n are the powers of respective prime factors.

So,
120= 2³ x 3¹ x 5¹
Factors=(3+1)(1+1)(1+1)=16.

Let the sum lent at 5% = P
? Sum lent at 8% = (1550 - P)
Then, [(P x 5 x 4)/100] + [{(1550 - P) x 8 x 4}/100] = 400
? 20P - 32P + 1550 x 32 = 40000
? - 12P + 49600 = 40000
? - 12P = - 9600
? p = ? 800
Sum lent at 8% = 1550 - 800 = ? 750
? Required ratio = 800 : 750 = 16 : 15