If we do 1 push up repetition per day, 3 sets, then increase it by one rep per week for same three sets, how many push ups will we be doing in 6months?
in case one push up repetition means two push ups, 3 sets will count 6 push ups
increasing one rep every week means A.P with first term of 6, common difference of 6 as well and 26 terms making 6 months
the answer should be sum=(26/2)*(2*6+25*6) that is 2106
A car has travelled 40 miles at 40mph.
It started its journey with 10 gallons of fuel but its tank has been leaking throughout the journey and is now dry.
The car completed 24 miles per gallon.
How many gallons of fuel does it leak per hour?
at 24 miles a gallon consumption by the engine for 40 miles=40/24 or 5/3 gallon
leaked fuel10-(5/3)=25/3 =8.3333 gallon
time of travel= 40/40= 1 hour
therefore rate of leakage=8.3333/1 =8.3333 gallon per hour
A car has travelled 50 miles at 70 mph.
It started its journey with eight gallons of fuel but its tank has been leaking throughout the journey and is now dry.
The car completes 25 miles per gallon.
How many gallons of fuel does it leak per hour?
since the consumption by engine is 50/25 = 2 gallons, it has leaked 8-2=6 gallons.
time to travel=50/70 hr = 5/7 hr
rate of leakage=6/(5/7)= 8.4 gallons per hour
Can you solve the below alphametic riddle by replacing letters of words by a number so that the below equation holds true?
BASE + BALL --------- GAMES (BASE) 7483 +
(GAMES) 14938
If possible.....
Thanks for the puzzle.
Let the number of cows be x, buffalo y and goat z.
Cost of three combined -
2x + y + 0.25z = 20
solving we get
8x + 4y + z = 160 ..... eqn (i)
Again, we know the number of animals is 20
hence,
x + y + z = 20 ...... eqn (ii)
Solving eqn (i) and eqn (ii) we get,
4x - 3z = 0
or 4x = 3z
i.e. x/z = 3/4
or the number of cows and goats are in the ratio of 3:4
taking Cows as 3 and goats as 4 we get buffaloes as 13
Which satisfies the conditions.
A 440 yard long train, travelling at 60 mph, enters a one mile long tunnel.
How long will elapse between the moment the front of the train enters the tunnel and the moment the end of the train clears the tunnel?
Answer : 1 minute and 15 sec.
Train is .25 mile long; traveling 60 miles per hour.
so; the front of the train will take 1 min to reach to the end of the tunnel. Body of the train is 1/4 mile; it will take 15 seconds to clear the tunnel.
A dinner party is to be fixed for a group consisting of 100 persons. In this party, 50 person do not prefer Veg, 60 prefer Non-veg and 10 do not prefer either Non-veg or Veg.
How many people prefer both Veg and Non-veg?
Lets assume A is the set of Veg people and B is the set of Non-Veg People
n(A U B) = 100 - 10 = 90
n(A) = 100 - 50 = 50
and n(B) = 60
Therefore
n(A Inter B) = n(A) + n(B) - n(A U B)
= 50+60 - 90
= 20
So 20 people prefer veg and non-veg both.
Volume of each rod = Pi * r * r * l
r = 2cm/2 i.e. 1cm or .01 m
l = 7
So volume of rod = (22/7) * .01 *.01 * 7 = .0022 cubic m
Metal volume = .88
Number of possible rod = .88/.0022 = 400
Answer: 400 rods are possible
194040 has factors of 2,2,2,5 and 4951 all of which are prime numbers and their sum is 4970
use A=sqrt(s*(s-a)*(s-b)*(s-c)) for area of a triangle which is 774.5966
hence area of parallelogram is 2*774.5966 or 1549.1933 sq m
a+b+c=odd
b+c+d=odd ADD
a+2b+2c+d=even
a+d=even
Given x is a real number, If SQRT(x+15) + SQRT(x)=15 then find the value of x.
It infers sqrt(x+15)=15-sqrt(x) square both sides
x+15=225+x-30*sqrt(x) or
sqrt(x)=7 or x=49 substitute in the statement o.k.
The ratio between the present ages of Pawan and Rohan is 5:7 respectively.
If the difference between Rohan’s current age and Pawan’s age after 6 years is 2.
What is the sum of Pawan & Rohan current age?
R/P=5/7
R-(P+6)=2 OR R-P=8 Substitute above relation
R-5R/7=8 or 2R/7= 8 giving R=28 and P=20
How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 0, which are divisible by 5 and none of the digits is repeated?
Looks 36. Ending with 0 we have to select two others from 5 which means 5P2=20. Similarly ending with 5 we have another 20 of which 4 starting with zero must be excluded. Hence 20+16=36
1^3^4^5 = 1
9^2^(-1) = 9^(1/2) = sqrt of 9 = 3.
Rohit went to buy some expensive, foreign chocolates. He only had Rs 100 with him. When he reached the shop, he got to know that on those chocolates, there was a 15% import duty and 5% VAT.
How much worth chocolate should he buy so that he can accommodate it in Rs 100 ?
If the VAT is added on the base price + Import Duty then
He would be able to buy chocolates worth Rs. 82.816
82.816 + Import Duty @ 15% Rs.12.422 = 95.238
Add 5% VAT on 95.238
Rs. 4.762
95.238 + 4.762 = 100
There is 40% increase in an amount in 8 years at simple interest. What will be the compound interest of Rs. 1,600 after 3 years at the same rate?
Simple interest comes 40/8=5 %. Amount from principal of 1600 at 5% for three years becomes 1600*1.05^3=1852.20. Therefore compound interest comes Rs. 252.20
The difference between simple interest and compound interest on a sum for 2 years at 8%, when the interest is compounded annually is Rs.16. If the interest were compounded half yearly, then what would be the difference between simple interest and compound interest for the same sum in 2 years?
the difference between the compound interest and simple interest for 2 yearsmay be arrived in the form PxRXR/10000.
R=8,solving get P=2500
Simple interest for the amount=400
comp interest =416
comp interest half-yearly =424.65
hence difference =24.65
Tn = [a + (n-1)d]
Sn = n/2*[2a +(n-1)d].
Given
T30/T10 = 3
(a + 29d)/(a + 9d) = 3
After simplification we get
a = d
S6 = 6/2 [2a + 5d] = 42 (given)
14 = 2a + 5d
14/7 = 2 = a = d ( substituting a = d)
So the series starts like
2, 4, 6, 8, 10, 12, 14, 16, .......
Now T13 = [2+12d] = [2 + 24] = 26.
< /a>pl see the explanationA+B=225;; A+B=180+45 ;; -45=180-(A+B) ;; TAKING TAN BOTH SIDES ;;; TAN(-45)=TAN(180-(A+B));;; -1=-TAN(A+B);;
TAN(A+B)=1 ;;; TAN(A) + TAN(B) = 1- TAN(A)TAN(B) ;;; TAN(A)+TAN(B)+TAN(A)TAN(B) = 1 ;; Question was to find {1+TAN(A)}{1+TAN(B)} === 1+ TAN(A) +TAN(B) + TAN(A)TAN(B) == 1+ 1 == 2 Assuming a person can grow a maximum of 40 crore hair on thier body and that the world has a population of 730 crore, What are the chances of 2 people having the same number of body hair on them ?
Looks 1/40 crore. Let the first person grow any number say n of hair. Second person can be anybody growing any number from 1 to 40 crore. The probability of n appearing in 40 crore is 1/40 crore.
The probability here as asked "exactly"
Is actually this
Now , as we know that a leap year has 366 days
This means if we want to have exactly 52 Tuesdays then the remaining two days must not be a Tuesday
The outcomes can be either
(Sun,Mon) (Mon,Tues),(Tues,wed) (Wed,thurs) (thurs,fri) (fri,sat)
(Sat,sun) .now the favourable outcomes are only 5 , therefore it should be 5/7
It is 5/7
Nevertheless I have used a spread sheet to find the 4P3 i.e. 24 three digit numbers. Each column has any digit 6 times. Hence the total of any column is 6*(3+4+6+8) i.e. 126. Writing 6 in the unit place we carry 12 to the second column which again has a total of 126 which makes it 126+12=138. We write 8 in the tens place and carry 13 to the third column. The third column will be 126+13=139 which we have to write as it is. Hence the answer reads 13986.
In a rational number,
twice the numerator is 2 more than the denominator.
If 3 is added to each i.e. the numerator and the denominator, the new fraction is 2/3.
Find the original number?
let the numerator be a and the denominator b. One of the equations is 2a=b+2. The other equation is (a+3)/b+3)=2/3. The solution gives a=7 and b=12. First check 2*7=12+2. Second check (7+3)/(12+3)=2/3
Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively.
What is the ratio of their speeds?
Let the distance between Howrah and Patna be D kilometer and let the trains cross at a distance of x from Howrah. Let us call the train from Howrah to Patna as T1 and other T2 and their corresponding speeds s1 and s2. The remaining distance in case of first train is D-x and in the other x. Since the first train covers its remaining distance in 9 hours and the other in 16 hours s1=(D-x)/9 similarly s2=x/16............(1)
There fore s1/s2=16*(D-x)/(9*x)
Since the two train cross after equal time from the start, their distances covered are in proportion to their speeds.
This gives s1/s2=x/(D-x).................(2)
From equation (1) and (2)
x/(D-x)=s1/s2=16s2/9s1
Cross multiplying gives s1/s2 = 4/3
If length, breadth and height of a room are in the ratio 3:2:1. If the breadth and length are halved, while the height is doubled. Then what is the percentage change in the total area of the 4 walls of the room?
