Maths

(d):3515.2 – 3380 = 135.2 = SI on Rs. 3380 for one year.

By SI formula, 135.2 = $3380*R*\frac{1}{100}$ $\frac{}{}$ or R = 4 %

Now we have 3380 = P (1.04)2 or P = Rs. 3125

(c):Let speed of passenger train be x m/s.

$\left[\left(\frac{66+88}{8.33+x}\right)\right]=0.168*60$

$\left[30*\frac{5}{18}=8.33\right]$

x = 6.94 m/sec = 25 kmph.

(c):We have 4 men = 5 women 1 man = $\frac{5}{4}$ $\frac{}{}$ women, 2 women = 4 boys, 1 women = 2 boys $\frac{5}{4}$ $\frac{}{}$ women = 2 * $\frac{5}{4}$ $\frac{}{}$ boys = $\frac{5}{2}$ $\frac{}{}$ or 1 man = $\frac{5}{4}$ $\frac{}{}$ women = $\frac{3}{2}$ $\frac{}{}$ boys

Now 2M + 3W+ 4B = 2 * B + 3 * 2B + 4B = 15 B Boys

Or 15 Boys do the work in 10 days (10 hectares) 6M + 4W + 7B = (6 * + 4 * 2 + 7) B = 30

Boys 30 boys will do 16 hectares of work in 8 days.

Let he offered 'n' different flowers

October has 31 days

ⁿC₄  ³ 31

Minimum value of n can take 7

Total numbers of ways = 5 * 6

Numbers of ways in which men can sit such that no men sat to the left of the women from his team i.e. Derangement of 6

D6 = $6!\left[\frac{1}{0!} +\frac{1}{1!} +\frac{1}{2!} +\frac{1}{3!} +\dots \dots \dots \frac{1}{6!} \right]$

= 265

F (0) = 5 * 265

Probability = $\frac{5!*265}{6!*5!}=\frac{53}{144}$

(d)   :  4¹¹ + 4¹² + 4¹³ + 4¹⁴ + 4¹⁵

= 4¹¹ (1 + 4¹ + 4² + 4³ + 4⁴) = 4¹¹ * 341.

The factors of 341 are: 1, 11, 31 and 341. Thus, we can say that the values in each of the three options would divide the expression.

It is given average of 24 numbers = 59.5

Sum = 59.5 *24 = 1428

Let the numbers erased be 'm'

1428 + m = $2\left(n*25+\frac{25*26}{2}\right)$

1428 + m = 50n + 650

50n – m = 778

Least value 'n' can take 16

(i) for n = 16, m =22

Series 2 (17, 18… 41)

i.e. 34, 36, 38 ….82

from this series we cannot remove 22. So, this case is not valid.

(ii) for n = 17, m = 72

Series 2 (18, 19… 42)

Only this case is valid

Average (A) = $\frac{\left(36+84\right)}{2}$ = 60

Sum of series after removing 72 and adding next consecutive even number

1500 – 72 + 86 = 1514

Average (C) = 1514/25 = 60.56

A – C = 60 – 60.56

= 0.56

(b):If X be the distance, we have:

$\frac{\left(\frac{X}{3}\right)}{10}+\frac{\left(\frac{X}{3}\right)}{9}+\frac{\left(\frac{X}{3}\right)}{8}+\frac{\left(\frac{1}{2}\right)}{60}=\frac{\left(\frac{X}{2}\right)}{10}+\frac{\left(\frac{X}{2}\right)}{8}$ or

X = 27 km.