Lets the number taken as 10A + B

After reversing the number 10B + A

10A+ B + 10B + A = 88

A + B = 8

Sum of the digits in a number itself is always equal to the sum of the number and the number formed by interchanging the digits.

Multiples of 5 end a number with 5 or 0; here the unit digit is 6

6 – 5 =1

Hence the remainder is 1

Given

2 × (1 + 2 + 6 + 24 + 120 + 720 + 5040)/6

= (1 + 2 + 6 + 24 + 120 + 720 + 5040)/3

Make 1 + 2 is a pair so that it can be divisible by 3

So, (1 + 2) , 6 , 24 , 120 , 720 , 5040  all are completely divisible by 3

So the reminder is 0.

Let principal 100

So,

1^st 10% = 10×1

2^nd 11% = 11×1

3^rd 12% = 12×1

4^th 13% = 14×1

5^th 14% = 15×1

SI = 60

Given SI is 3600

So 60 unit = 3600

1 unit = 60

So principal is 100×60 = 6000

Time taken to fill the tank - 3 hours

Time taken to fill the tank with leakage – 4 hours

So,

Let we consider 12 (LCM of 3 and 4) as total work then

Efficiency when pipe fill the tank alone 12/3 = 4

Efficiency when pipe and leakage fill tank 12/4 = 3

It means efficiency of leakage is 4 – 3 = 1

So the time taken by the leakage to empty the tank is 12/1 = 12 hours

Ratio of present age of sakshi and divya = 4 : 5

Let the present age of Sakshi and Divya = 5x and 4x

So 5 years hence there age

Sakshi: 5x+5

Divya: 4x+5

So from the given information,

(5x+5) - (4x+5) = 3

5x+5 – 4x – 5 = 3

x = 3

So their ages are = Sakshi = 5×3 = 15, Divya= 4×3 = 12

So the sum of their ages = 15 + 12 = 27

Let the price of table is 100

Discount %= 20%

So the price at which Rakesh bought = 100 – 100×20% = 80

Rakesh sold the table at 20% profit on the table’s original price

Selling price of the table = 120% of the price of the table

= 120%×100 = 120

So profit of Rakesh is SP – CP = 120 – 80 = 40

So,

Profit percentage = 40/80×100= 50%

Tan (3θ + 45⁰) = Tan (90⁰ – 2θ)

 3θ + 45⁰ = 90⁰ – 2θ

5θ = 45⁰

2θ = 18⁰

4 × 25/5 – 20×2 + 45

20 – 40 + 45= - 20 + 45= 25