Job Roles

Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.
Area of each tile = (41 x 41) sq.cm

Required number of tiles =1517 x 902/(41 x 41) = 814.

Given there are 2 coloured socks, which is black and White
Let suppose 3 is choosen at random
then three conditions arises
1. all are black
2.all are white
3. either it will have 2 black and 1 white or it will have 2 white and 1 black
so in all the conditions as above mentioned we are getting atleast one pair of socks.

So, he must take out 3 to be sure that he has a matching pair.

Clearly, while counting the numbers associated to the thumb will be 1,9,17,25,.........
i.e., numbers of the form (8n + 1 ).
where n=1,2,3...
Since 1994 = 249 × 8 + 2, so 1993 shall correspond to the thumb and 1994 to the index finger and 1995 to the middle finger.

2 engines of former type for one hour consumes (2 x 24)/(6 x8) = 1 metric ton 

i.e. 3 engines of latter type consumes 1 ton for one hour

Hence 9 engines consumes 3 tons for one hour

For 15 hours it is 15 x 3 = 45 metric tonnes.

Let the C.P be 'x'
Then, the selling price S.P = x - 16x/100
= 84x/100 = 21x/25
Now, if the S.P is 60 more, then the profit is 14%
=> 21x/25 + 60 = x + 14x/100
=> 114x/100 - 21x/25 = 60
=> (57 - 42)x/50 = 60
=> 15x/50 = 60
x = 3000/15 = 200

Therefore, the Cost price C.P = x = Rs. 200

Let C.P.= Rs. 100.
Then, Profit = Rs. 320,
S.P. = Rs. 420.

New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420.

Profit = Rs. (420 - 125) = Rs. 295

Required percentage = (295/420) * 100
= 70%(approx)