Running at a speed of 60 km/h, a train passed through a 1.5 km long tunnel in 2 min. What is the length of the train?

Total number of ways of filling the 5 boxes numbered as (1, 2, 3, 4, and 5) with either blue or red balls 2⁵ = 32.
Two adjacent boxes with blue can be obtained in 4 ways, i.e., (12), (23), (34) and (45).
Three adjacent boxes with blue can be obtained in 3 ways, i.e., (123), (234)and (345). Four boxes with blue can be obtained in 2 ways, i.e., (1234) and (2345). And five boxes with blue can be got in 1 way. Hence, the number of ways of filling the boxes such that adjacent boxes have blue
= (4 + 3 + 2 + 1) = 10.
Hence, the number or ways of filling up the boxes such that no two adjacent boxes have blue = 32 - 10 = 22.

Give, time = 42 months.
= (42/12) yr = 3¹/₂ yr
= 7 half - yr,
rate = 13/2% half - yearly

SI = (20000 x 13 x 7)/(100 x 2) = ? 9100
? Amount (A) = 20000 + 9100
= ? 29100

(52 - 33) = 19, (78 - 59) = 19 and (117 - 98) = 19
LCM of 52, 78 and 117 is 468.
Required least number = 468 + 19 = 487
Sum of digits of 487 = 4 + 8 + 7 = 19

The length of the fast train = Relative speed x Time
= (40 - 20) x (5/18) x 5 = 27⁷/₉ m

Let us draw a figure below from given question.
Let AB = h meter be the height of the tower B and C are two points such that ?ACB = 30° ?ADB = 45° and CD = x meter (say)
From right triangle ABD,
tan 45° = h/BD
? BD = h meter;
Again from right triangle ABC
tan 30° = h/(h + x )
? h + x = ?3 h
? x = (1.73 - 1)h = 0.73h
Now, 0.73h meter covered in 12 min
Hence, h meter covered in 12/0.73 = 1200/73 min = 16 min 23 sec .

The largest possible number of persons in a class is given by the H.C.F. of 391 and 323 i,e. 17

? No of classes of boys = 391/17 = 23 and
No. of classes of girls = 323 / 17 = 19.

Let LCM = m, HCF = n,

According to the question,
m = 12n, .......(i)
and m + n = 403.......(ii)
? 12n + n = 403 [from Eq.(i)]
? 13n = 403
? n = 403/13 = 31
? m = 12 x 31 = 372

Let the another number = k
? 93 x k = 372 x 31
[as product of two numbers HCF x LCM]
? k = (372 x 31)/93 = 124

If interest is 40% of the principal then time = 5 years.
So, when interest would be equal to 100% of the principal time would be
= (100/40) x 5 years = 12.5 years
= 12 yr 6 months

A = ? 3400 T = 3 yr , R = 1% per month = 12 % per annum Let the principle be ? P.
SI = (PTR/100) = (P x 3 x 12)/100 = ? 36P/100
A = (P + SI) = P + 36P/100 = ? 136P/100
? 136P/100 = 3400
? P = (3400 x 100)/136 = 2500
? Sum = ? 2500