Suppose that x glassses are supplied safely , therefore
(100-x) glases are damage. Then equation is :
3x – 3(100-x) = 270
on solving this equation value of x comes out to be 95.
2years
9654
6561 → 6560/2 [-1]
3280
1640
820
410
205 [+1] =206
103 → [-1] = 102
51 [+1] = 52
26
13 [-1] = 12
6
3 [+1] 4
2
1
1000
The work done by A in 8 days is = 8/ 12 = 2/3
Means A alone completes 2/3 part of work.
Remaining work which is (1–2/3) = 1/3 is completed by B in 8–2 = 6 days
So the complete work done by B in 6/(1/3) = 18 days.
B alone can complete the work in 18 days.
d
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
2:3:4
Let d = 7r. And use distance is = rate × time
7r= ( r+12) 5
7r= 5r + 60
Subtract 5r from both sides
2r = 60
Divide out 2
Rate = 30 km/h
Original question 30 km/h × 7 = 210
30 +12 = 42× 5 = 210
1.5 km/hour
slower train – 48 kmph = 40/3 m/s
say faster train, v m/s
therefore, {v-(40/3)}*180 = 600, => v= 60 kmph
How breadth is 19.84..?
Apply Pythagoras therom,
a^2+b^2=c^2,
Lets Assume
c is hypotenuse or diagonal,
a is length or opposite side,
b is breadth or adjacent side,
Then,
256+b^2=400
b^2=144
b=12,
So the breadth is 12 cm
I would design a voice integrated clock that reads out the time aloud whenever people ask for time
B. No such pair exists
8+3+4=15
15+(7)=22
22 is divisible by 11.
So,7 is right answer. Option C
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