A man gained 10% by selling an article for a certain price. If the sells it at double the price, then the profit made is?

In a game of 50, If A scores 50 then B scores 44.
? A scores 65 while B 44 * 65 / 50 = 57.2 points
Now, B scores 57.2 points while C 52
? B scores 55 points while C = 52 * 55 / 57.2 = 50
Hence, in game of 55 points B can give C (55 ? 50) = 5 points

Weight of new person = (65 + 20) kg = 85 kg.

Total number of rounds made by Ram in 15 / 4 hrs = 5 × 15 / 4 = 75 / 4
? Total number of rounds made by Karan in 15 / 4 hrs = 36 / 7 * 15 / 4 = 135 / 7
Total number of rounds made by Mohan in 15 / 4 hrs = 16 / 3 * 15 / 4 = 20
H.C.F. of 75 / 4 , 135 / 7 and 2 = 5 / 28

?5 + 2?6 - 1/?5 - 2?6
= ((?5 + 2?6 x ?5 - 2?6 ) - 1)/?5 - 2?6

Apply the formula of Algebra.
( a + b ) x (a - b ) = a² - b²
= (?(5)² - (2?6 )² - 1)/?5 - 2?6
= (?25 - 4 x 6 - 1) /?5 - 2?6
= (?25 - 24 - 1) /?5 - 2?6
= (? 1 - 1 )/?5 - 2?6
= (1 - 1 )/?5 - 2?6
= 0/?5 - 2?6
= 0

Method 1
Let us assume the ratio factor is x.
Therefor the present ages of Vikas and Vishal be 15x years and 8x years.
After 10 years
vikas's age = 15x + 10 and Vishal' age = 8x + 10
According to question,
(15x+10)/(8x+10) = 5/3
? 3(15x + 10) = 5(8x + 10)
? 45x + 30 = 40x + 50
? 5x =20
? x = 20/5
? x = 4
Therefore Present age of Vikas = 15x = 15 x 4 = 60 years
and Present age of Vishal = 8x = 8 x 4 = 32 years

Method 2
Let us assume the present age of Vikas = x years and Vishal's present year = y years
According to question,
Present age of Vikas/ Present age of Vishal = 15/8
? x/y = 15/8
? 8x = 15y
? 8x - 15y = 0
? x = 15y/8 .................................(1)
After 10 years Vikash age = x + 10 and vishal age = y + 10
Ratio of age after 10 years = 5/3
(x + 10)/(y + 10) = 5/3
? 3(x + 10) = 5(y + 10)
? 3x + 30 = 5y + 50
? 3x - 5y = 50 - 30
? 3x - 5y = 20 ................................(2)
Put the value of x from equation (1) in above equation (2).
? 45y/8 - 5y = 20
? 45y - 40y = 20 x 8
? 5y = 20 x 8
? y = 4 x 8 = 32
Put the value of Y in equation (1)
x = 15 x 32/8 = 15 x 4 = 60

Therefore Present age of Vikas = x = 60 years
and Present age of Vishal = y = 32 years

Method 1 to solve this question.
Let us assume the numbers of days of tour before extending the tour are D and daily expenses is E.
According to question,
Total expenses on tour = per day expenses x total number of days
Total expenses on tour = E x D = ED
360 = ED
? ED = 360
? E = 360/D .................(1)
Again according to question,
After extending the tour by 4 days, Number of days of tour = D + 4
Expenses will be reduced by 3 rupees, then everyday expenses = E - 3
so total expenses = (D + 4) x (E - 3)
360 = (D + 4) x (E - 3)
(D + 4) x (E - 3) = 360 .............................................(2)
Put the value of E in Equation (2). we will get,
(D + 4) x (360/D - 3) = 360
? (D + 4) x ( (360 - 3D)/D ) = 360
? (D + 4) x ( (360 - 3D) ) = 360 x D
? (D + 4) x (360 - 3D) = 360 x D
After multiplication by algebra law,
? 360 x D - 3D x D + 4 x 360 - 4 x 3D = 360D
? 360 x D - 3D + 1440 - 12 D = 360 D
? - 3 D + 1440 - 12 D = 360 D - 360 x D
? - 3 D + 1440 - 12 D = 0
? 3 D - 1440 + 12 D = 0
? D - 480 + 4 D = 0
? D + 4 D - 480 = 0
? D + 24 D - 20 D - 480 = 0
? D( D + 24) - 20( D + 24) = 0
? ( D + 24) ( D - 20) = 0
Either ( D + 24) = 0 or ( D - 20) = 0
So D = - 24 or D = 20
But days cannot be negative so D = 20 days.

Method 2 to solve this question.
Let us assume the original day of tour is d days.
Given that his tour is extended for 4 days
Hence daily expenses per days = 360/(d + 4)
Therefore, According to question,
360/d - 360/(d + 4) = 3
? (360(d + 4) - 360d)/d x (d + 4) = 3
? (360(d + 4) - 360d)/d x (d + 4) = 3
? 360(d + 4) - 360d = 3d x (d + 4)
? 360d + 1440 ? 360d = 3(d ² + 4d)
? 1440 = 3d ² + 12d
? 3d ² + 12d ? 1440 = 0
? d ² + 4d ? 480 = 0
? d ² + 24d ? 20d ? 480 = 0
? d(d + 24) ? 20(d + 24) = 0
? (d + 24)(d ? 20) = 0
? (d + 24) = 0 or (d ? 20) = 0
? d = ?24 or d = 20
Since days cannot be negative, d = 20
Hence his original duration of the tour is 20 days.

For n =1
7⁶ⁿ - 6⁶ⁿ = 7⁶ - 6⁶
? ( 7³ )² - ( 6³ )²
? ( 7³ - 6³ )( 7³ + 6³ )
= ( 343 - 216 )( 343 + 216 )
= 127 x 559

? it is clearly divisible by 127.

L.C.M. of 252, 308 and 198 = 2772 seconds
= 46 × 60 + 12 = 46 min 12 seconds.
.

Solving the question by taking two odd numbers greater than 1 i.e. 3 and 5,
for n =3, n( n² -1 ) = 3( 9 - 1) = 24
for n = 5 n( n² -1 ) = 5( 25 - 1) = 120

Using option we find that both the number are divisible by 24.