Given N = 10p78pq is exactly divisible by 120.
Since the last digit of the dividend is 0, the last digit of N also should be 0.
Then obviously, q = 0.
i.e., N = 10p78p0
Now we have to find p.
We know 120 = 3 x 5 x 8 and 3, 5 and 8 are co-primes.
If N is divisible by 120 then it is divisible by 3, 5 and 8.
We know that, "If a number is divisible by 3 then the sum of its digits also divisible by 3"
Then, 1+ 0 + p + 7 + 8 + p + 0 = 16 + 2p
i.e., 16 + 2p must be divisible by 3
Then the possible values of p are 1,4,7,10,13 and so on
Since p is a digit, the possible values are 1, 4, 7
Now, N must be divisible by 8 also.
We know that, "If a number is divisible by 8 then its last 3 digits also divisible by 8"
Here 8p0 is a multiple of 8.
Now put all the above possible values of p then we have 8p0 = 810 or 840 or 870
From these, 840 is a multiple of 8.
Then the value of p = 4 and N = 1047840
Hence, the required sum = 1 + 0 + 4 + 7 + 8 + 4 + 0 = 24.
Let S be the sample space. Then,
n(S) = 52C2 = (52 × 51)/(2 × 1)
= 1326.
Let E = event of getting 2 queens out of 4.
n(E) = 4C2 = (4 × 4)/(2 × 1)
= 6.
P(E) = n(E) / n(S) = 6 / 1326
= 1/221.
Every such number must be divisible by L.C.M of 4, 5, 6 i.e., 60.
Such numbers are 60,120,180,240,300,360... 960.
Clearly, there are 16 such numbers.
Let the Sum be ’P’.
Given, P(1 + 20/100)2 - P = 176
Solving for P, we get P = 400.
Now, P = 400, T = 4 years, R = 10%
S.I = (400 x 4 x 10) / 100 = 160
Thus, the required simple interest is Rs.160.
Let the number of ducks be d and number of cows be ’c’.
Then, total number of legs = 2d + 4c = 2(d + 2c)
Total number of heads = c + d.
Given that total numbers of legs are 14 more than twice the number of heads.
=> 2(d + 2c) = 14 + 2(c + d).
=> 2d + 4c = 14 + 2c + 2d.
=> 2c = 14
=> c = 7
i.e., total number of cows = 7.
LCM of 2-4-6-8-10-12 is 120 seconds that is 2 minutes.
Now 60/2 = 30
Adding one bell at the starting it will be (30+1) = 31.
0.8 C.P=16
C.P=20
In order to make a profit of 10%
The selling price should be 10% of 20 = 2
So the selling price should be -----> 20+2 = Rs.22.
{(3 * 2.333 + 2)/3} / (1/10 of 100 + 4.8181) = {(6.999 + 2)/3} / (10 + 4.8181) = {8.999/3} / (14.8181) = 2.999 / 14.8181 = 0.2023 And from the given options, 33/163 = 0.2024 Hence, 33/163 is the correct option from the given options.
$4^{6}$
Let the initial Price = Rs.100 and initial sales = 100
So, the initial revenue = Rs. 10000
Now, the price is reduced to 25% which is equal to Rs.75 and Sales is increased by 20% which is equal to 120.
Now new revenue = 120 x 75 = Rs. 9000
Change in revenue = (10000 - 9000) = Rs.1000 decrease
% decrease = (1000/10000) x 100 = 10%
Hence, the correct option is decrease of 10%.