The average age of women and child workers in a factory was 15 yr. The average age of all the 16 children was 8 yr and average age of women workers was 22 yr. If 10 women workers were married, then the number of unmarried women workers was.

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