A moneylender finds that due to a fall in the rate of interest from 13% to 12 ¹/ ₂% his yearly income diminishes by Rs. 104. His capital is?

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.