Question

1. At what time between 9 and 10 o'clock will the hands of a watch be together?
(A). 50 min. past 9
(B) 49 whole 1/11 min. past 9
(C) 48 whole 1/7 min. past 9
(D) 48 whole 2/7 min. past 9

2. In a certain code, MUMBAI is written as 434219, how is HARYANA written in that code?

A. 8197151

B. 8195171

C. 8175141

D. 8196141

Answer 1

Answer:

1.(b), (49 whole 1/11 minute, past 9)

2.(a), (8197151)

Explanation:

❤

Answer 2

Question 1.

Answer;

(B) 49 whole 1/11 min. past 9

$\star$ Solution:

Originally at  9'o clock hour hand will be at  9

And the minute hand will be at  12.

So,

In  1  hour, an hour hand gains angle = $\red{30^{o}}$

In  1  minute, a minute hand gains = $\frac{30^{o}}{5}$ = $\red{6^{o}}$

So,

The angle obtained by hour hand at any time

= $\boxed{\boxed{\red{30[y+(\frac{x}{60})]^{o} }}}$

So,

The angle that is obtained by minute hand = $\blue{(6x)^{o}}$

Whereas, '$\blue{y}$' is the number of an hour hand so, In question, it is 9

And '$\blue{x}$' is the minutes after the '$\blue{y}$' O' clock.

$\underline{According\ to\ the\ question:}$

$\implies 30[y+\frac{x}{60}] = 6x$

$\implies30[9+\frac{x}{60}] = 6x\ \ \ [\therefore y=9]$

$\implies 270 + \frac{x}{2}=6x$

$\implies \frac{540+x}{2}=6x$

$\implies 540+x = 12x$

$\implies 540=12x - x$

$\implies 540=11x$

$\implies \frac{540}{11} = x$

$\implies \boxed{x = 49\frac{1}{11}\ \rm min.}$

Hence,

The hands are together between 9 and 10'o clock, the minute hand has to gain 45 min. spaces.

So,

Minutes hand gains 55 min spaces in 60 min.

Now,

$\rm 45min\ spaces\ will\ be\ gained\ in$

$\sf (\frac{60}{55}\times 45)\ min\ or\ 49 \frac{1}{11}\ min.$

∴ The hands are together at $\sf 49\frac{1}{11} min.\ past\ 9$

- - - - -

Question 2.

Answer -

A. 8197151

$\star$ Solution:

Given:

For MUMBAI = 434219

So,

M = 13 = 1+3 = 4

U = 21 = 2+1 = 3

M = 13 = 1+3 = 4

B = 2

A = 1

I = 9

So.

For HARYANA, we get,

H = 8

A = 1

R = 18 = 1+8 = 9

Y = 25 = 2+5 = 7

A = 1

N = 14 = 1+4 = 5

A = 1

Hence

For HARYANA the certain code will be 8197151