Required Ratio=3:2
Ans is 25
To determine how many consecutive zeros the product of S will end with, we need to find the highest power of 10 that divides the product. This is equivalent to finding the highest power of 5 that divides the product, since the number of factors of 2 will always be greater than the number of factors of 5.
The primes in S are {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}.
There are 24 primes in S, so the product of S is:
2 x 3 x 5 x 7 x 11 x 13 x 17 x 19 x 23 x 29 x 31 x 37 x 41 x 43 x 47 x 53 x 59 x 61 x 67 x 71 x 73 x 79 x 83 x 89 x 97
We need to find the highest power of 5 that divides this product. To do this, we count the number of factors of 5 in the prime factorization of each number in S.
5 appears once: 5
5 appears once: 25
5 appears once: 35
5 appears once: 55
5 appears once: 65
5 appears once: 85
So, there are six factors of 5 in the product of S. However, we also need to consider the powers of 5 that arise from the factors 25, 35, 55, and 65.
25 = 5 x 5 appears once: 25
35 = 5 x 7 appears once: 35
55 = 5 x 11 appears once: 55
65 = 5 x 13 appears once: 65
Each of these numbers contributes an additional factor of 5 to the product of S. Therefore, there are 6 + 4 = 10 factors of 5 in the product of S.
Since each factor of 5 corresponds to a factor of 10, we know that the product of S will end with 10 zeros. Therefore, the product of S will end with 10 consecutive zeros
Since the car has met the person 20 minutes beforehand, it has saved 10 mins of a journey
A man has started 1.30 hrs before and the car has met him 10 mins before the actual time, he takes to reach daily is 1hr and 20 mins
time = distance / speed
speed = 36*(5/18) m/s=10m/s
distance = 100m
time=100/10s = 10sec
Artificial silk
430
5x5x6 = 150 cube
150 – 20( corner cube) = 130 cube
130 x 3 (side remaining) = 390
20 x 2 (side remaining) = 40
total side remaining = 390 + 40 = 430
600
(3/4)*(L/Sp)=30
L/Sq=75
(3/4)*(Sq/Sp)=30/75
Sq/Sp=8/15
Sp/Sq=15/8
2880, 480, 92, 24, 8, 4, 4
4×1 = 4
4×2=8
8×3=24
24×4= 96 (not 92)
96×5 =480
480×6= 2880
So answer is 92
T is the last speaker.
2:3
65 KM
5 litre jug contains 4 litres of salt water solution
with 15% of salt, that means it has 4000*.15 = 600 ml salt
in it.
If 1.5 litres solution is spills out, remaining solution
is 2.5 litres, then the salf content is 2500*.15 = 375ml.
Now, the jug is filled to full capacity with water i.e.,
now the jug has 5 litre solution in it.
Now, the salt content is 375/5000 = 7.5%
C