The wall clock makes 1 beep when it shows time 1.
It makes 2 beeps when it shows time 2.
Similarly, it makes 12 beeps when the time is 12.
Then the total number of beeps = 1 + 2 + 3 + ... + 12
1, 2, 3,...12 is series of natural numbers from 1 to 12. Hence totally 12 terms.
We know that, the sum of n natural numbers is [n(n+1)]/2= (12*13)/2 = 78
That is, it makes 78 beeps in 12 hours.
Since a day has 24 hours, then the required number of beeps = 2 x 78 = 156.
Given that, average of P, Q, R = 51 $\dfrac{2}{3}$ = 155/3
i.e., (P + Q + R ) / 3 = 155/3
Then, P + Q + R = 155.
Average of seven values = (P + Q + R + P + Q + R + P + Q + Q + R + R + P) / 7
= [(P + Q + R) + (P + Q + R) + (P + Q + R) + (P + Q + R)] / 7.
= [155 + 155 + 155 + 155 ] / 7
= 620 / 7 = 88.57
Hence, the required average is 88.57
Area of a square with side a = $a^{2}$
Here, a = 12 inches then $a^{2}$ = 144
Area of an equilateral triangle with side b = ($sqrt^{3}$)($b^{2}$)/4.
Here, b = 12 inches then (sqrt3)($b^{2}$)/4 = (sqrt3)(144)/4 = 36(sqrt3)
Now, the required relation = Area of the square / Area of the triangle
= 144 / [(sqrt3)36] = 4/sqrt3.
Suppose B alone takes X hours to fill the tank.
Then, A takes = 1/2 of 3X = 3X/2 hours.
Now, B’s 1 hours work = 1/X and A’s 1 hours work = 2/3X.
Given that, (A + B) takes = 18 hours.
Then (A + B)’s 1 hour’s work = 1/18.
Therefore, 1/18 = 1/X + 2/3X.
5/3X = 1/18
X = 30.
Hence, B takes 30 hrs to fill the tank alone.
Take M = 100,
Then, Y = 50, N = 20, X = 6.
So, X/Y = 3/25
Gain in 2 years
= Rs. (5000 * 25/4 * 2) /100 - (5000* 2 * 2)/100
= Rs. (625 - 200)
= Rs. 425.
Gain in 1 year = Rs.425/2 = Rs. 212.50
18% per annum
ie) for 12 months the rate of interest is 18%
for 4 months the rate of interest is 6%
so for 8 months the rate of interest is 12%
The present worth of 12,880 (before 8 months) is 12,880/1.12=Rs.11,500
So when we compare the present worth of the two Rs.12,000 cash is better.
Total cost = Rs. [1 x 1000 + (100 - 2)% of 1 x 4000]
= Rs. (1000 + 0.98 x 4000)
= Rs. (1000 + 3920)
= Rs. 4920.
present ratio of ages= 25:20 = 5:4
3 years hence = 11:9
The difference in ratio after 3 years is 2. Hence multiply the 1st ratio by 2 to get the same difference: 10:8
Now the difference is same in both the ratio. here the ratio increases from 10 to 11 (ie: 1 part increase).
1 part is 3 years. Edwards present age is 10 parts
Hence edwards age is: 10*3= 30.
When number of days in a given period of time is divided by 7 then the remainder which results represents the number of odd days.
To start with consider a span of 100 years. Every 4th year is a leap year within a century and every 4th century year is a leap year.
This means years 4,8,12 etc are leap years while 100 is not a leap year.
But 400th year, 800th year etc are leap years.
By above argument 100 years contain 24 leap years and 76 non leap years. (Years 4,8,12....96 are leap years and 100th year is not. Therefore, number of leap years in 100 years is 100/4 - 1)
Number of days in 100 years = 24 x 366 + 76 x 365 = 36524
Dividing 36524 by 7, we will get a quotient of 5217 and remainder of 5.
Therefore, 100 years i.e., 36524 days has 5 odd days to end with. Since the century has started with monday, odd days in order will be Mon, Tue, Wed, Thu and Fri.
Last odd day will be the last day of the century. Hence, last day of 1st century will be Friday.
By similar ways one can find that 200 years will contain 3 odd days, 300 years will contain 1 odd day and 400 years will contain 0 odd days.
This means last day of 2nd century will be Wednesday, last day of 3rd century will be Monday and last day of 4th century will be Sunday.
The entire cycle will repeat for the next 400 years, thereafter next 400 years and so on.
Therefore, last day of the century cannot be Tuesday, Thursday or Saturday./p>