A moneylender lends Rs. 2000 for 6 months at 20% per annum whereas the interest is compounded quarterly. After the given period he will get the amount of?

Let sum be P.
? 50% of P = P/2 = SI
Now, P/2 = (P x 5 x T) / 100 [ as time = 10 yr]
? P/2 = 5PT / 100
? 1/2 = T/20
? = T = 10 yr

Increase in circumference of circle = 5%
? Increase in radius is also 5%.
Now, increase in area of circle = 2a + (a²/100) %
Where, a = increase in radius= 2 x 5 + (5 x 5)/100 % = 10.25%

Let the number of failed student = Y
? Number of passed student = 80 - Y

sum of marks of all students = sum of marks of passed students + sum of marks of failed students
80 x 40 = (80 - Y) x 60 + 35Y
? 3200 =4800 - 60Y + 35Y
? 25Y = 1600
? Y = 64
? Number of students who failed = 64

2 men = 7 boys
? 1 man = 7/2 days

5 women = 7 boys
? 1 women = 7/5 boys

7 men + 5 women + 2 boys = 7 x 7/2 + 5 x 7/5 + 2 = 67/2 boys
Now, B₁ x D₁ = B₂ x D₂
7 X 469 = 67/2 x D₂
D₂ = 98 days

Let the value for ? be N
So N x 9 x 7 x 3 = a number with unit digit 1.
Clearly, the minimum value of N is 9.

Given expression = [(272 - 32) (124 + 176)] / (17 x 15 - 15)
= (240 x 300 ) / 240
= 300

Average = (8 + 9 + 12 + 13 + 15 + 9)/6
= 66 / 6
= 11

? Relative speed of the train = 60 + 6 = 66 km/hr
= 66 x 5/18 m/sec = 55/3 m/sec

? Required time = 110 x (3/55) = 6 sec

Given, length of four metal roads are 78, 104, 117 and 169 cm.
Now,
78 = 13 x 2 x 3,
104 = 13 x 2 x 2 x 2,
117 = 13 x 3 x 3,
169 = 13 x 13

Length of each piece of rod as long as possible, HCF = 13 CM
? Number of piece = 6 + 8 + 9 + 13 = 36

Speed = 30 km/hr = 30 x (5/18) = 25/3 m/sec.
? Length of the train = (25/3) x (27/2)
= 225/2 = 112¹/₂ metres