Sunil complete a work in 4 days whereas Dinesh completes the work in 6 days. Ramesh work 1 ¹/ ₂ times as fast as sunil. How many days it will take for the three together to complete the work?

Given in the question,
Banker's Discount = 420
Time in years = 4 months = 4/12 years = 1/3 years
Rate of interest = 15 %
As we know the formula,
True Discount = Banker's Discount × 100 (100 + Time in years x Rate of interest )
True Discount = 420 × 100 (100 + 4/12 × 15) ( 12 Months = 1 Year)
= 420 × 100 (100 + 5) = 400

Since two digit number = 10p + q
According to question , ? q = 2p ? 1.. (i)
When digits are interchanged then new number = 10q + p
then original number ? [new number ? original number] = 20
? 10p + q ? [10q + p ? (10p + q)] = 20
? 10p + q ? 10q ? p + 10p + q = 20
19p ? 8q = 20
19p ? 8 (2p ? 1) = 20 (Using eq. (i))
19p ? 16p + 8 = 20
3p = 12 ? p = 4
From (i) q = 2 × 4 ? 1 ? q = 7
? original number = 10p + q = 10 × 4 + 7 = 47

Last digit will be multiplication of 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9.
It includes 5 & 2.
So, 5 x 2=10,
0 will be the last digit.

Age of the teacher = Sum of age of 24 students and teacher - Sum of age of 24 students.
= 25 x 11 - 24 x 10
= 35 years.
? Age of teacher = 35 years.

Position value of 6 = 10000

Let number be the x.
According to the equation , x - ^x?₇ = 180
? ^6x?₇ = 180
? x = 210

Let the two consecutive odd number be (x + 1) and (x + 3).
According to question (x + 1) (x + 3) = 6723
? x² + 3x + x + 3 = 6723
? x² + 4x + 3 = 6723
? x² + 4x - 6720 = 0
? x² + 84x - 80x - 6720 = 0
? ( x - 80 )( x + 84 )= 0
? x = 80, (x ? -84)
Hence, the greater number = 80 + 3 = 83

There can be infinite number of rational numbers between 1 and 1000.

Let 5 consecutive even number be A = x, B = x+2, C = x+4, D = x + 6 and E = x + 8.

According to question
x + x +2 + x + 4 + x + 6 + x + 8 = 130
? 5x + 20 = 130
? x = 22
? A = 22, E = 22 + 8 = 30.
? Multiplication of A and E = 22 x 30
= 660

The local value of 7 in 5679032 is 70000.