In a bangel shop, the shopkeeper displays the bangels in the form of a square, then he is left with 38 bangles with him. If he wants to increse the size of square by one unit each side of the square, he found that 25 bangles fall short of in completing the square. The actual number of bangles which he had with him in the shop was?

7.2 kg = 7.2 x 1000000 gm = 7200000 gms
Required percentage = (18/7200000) x 100 % = 0.25%

In 19683, 19 lies between 2³ and 3³, so left digit is 2 and 683 ends with 3, so right digit is 7.
thus 27 is a cube root of 19683.

Area of the field =1215/135 = 9 hec
= 90000 m² [1 hec =10000 m²]
? Side of the field = ?90000 = 300 m
Perimeter of the field = 4 x 300 = 1200 m

Now, cost of putting a fence around field = (1200 x 75)/100 = ? 900

Place value of 8 = 800
Face value of 8 = 8
? required sum = 800 + 8

Given equation is
a^-1 - 1
Apply the law of Fractional Exponents and Laws of Exponents
x^-y = 1/x^y
? a^-1 - 1 = 1/a - 1
? a^-1 - 1 = (1 - a)/a
Now divide by a - 1 in above equation,
? ( a^-1 - 1 ) ÷ (a - 1) = (1 - a)/a ÷ (a - 1)
? ( a^-1 - 1 ) ÷ (a - 1) = (1 - a)/a x 1/ (a - 1)
? ( a^-1 - 1 ) ÷ (a - 1) = -1x (a - 1)/a x 1/ (a - 1)
? ( a^-1 - 1 ) ÷ (a - 1) = -1/a
? Required quotient = -1/a.

Required number = LCM of (12, 15, 20, 24) + 2
= 120 + 2 = 122

According to the question,
Area of semi- circle = 77 m
(1/2) x ? x r² = 77
? r² = (77 x 2 x 7)/22
? r = 7m

?Circumference of semi- circle =?r + 2r
= ( ? + 2)r
= [(22/7) + 2] x 7
= 36 m

It is clear from expression is that remainder is 18

Let length, breadth and height be 4k, 3k and 2k, respectively.
Whole surface area = 2(lb + bh + lh)
? (lb + bh + lh) = 8788/2 = 4394
? (4 x 3 + 3 x 2 + 2 x 4 ) k² = 4394
? 26k² = 4394
? k² = 169
? k = 13
? Length = 4k = 4 x 13 = 52 cm

let us assume the ten's digit number be x and unit's place digit be y.
Then two digit Original Number = 10x + y
According to question ? y = 2x - 1 ................(1)
When digits are interchanged then new number = 10y + x
If the digits at unit's and ten's place are interchanged, the difference between the new and the original number is less than the original number by 20,
New Number - Original Number = Original number - 20
? 10y + x - (10x + y) = 10x + y - 20
? 10y + x - 10x - y - 10x - y = - 20
? 8y - 19x = - 20
? 19x - 8y = 20 ...................(2)
Put the value of y from equation (1) in above equation (2).
? 19x - 8(2x - 1) = 20
? 19x - 16x - 8 = 20
? 7x = 20 + 8
? 7x = 28
? x = 28/7
? x = 4
Put the value of y in equation (1)
From (i) y = 2 x 4 -1 = y = 7
? original number = 10x + y =10 x 4 + 7 = 47.