Frank solutions for Mathematics [English] Class 9 ICSE chapter 6 - Changing the subject of a formula [Latest edition]

The simple interest on a sum of money is the product of the sum of money, the number of years and the rate percentage. Write the formula to find the simple interest on Rs A for T years at R% per annum.

The volume V, of a cone is equal to one third of π times the cube of the radius. Find a formula for it.

The fahrenheit temperature, F is 32 more than nine -fifths of the centigrade temperature C. Express this relation by a formula.

The arithmetic mean M of the five numbers a, b, c, d, e is equal to their sum divided by the number of quantities. Express it as a formula.

Make a formula for the statement:"The reciprocal of focal length f is equal to the sum of reciprocals of the object distance u and the image distance v."

Make a formula for the statement:"The number of diagonals, d, that can be drawn from one vertex of an n sided polygon to all the other vertices is equal to the number of sides of the polygon less 3"

The area A of a circular ring is π times the difference between the squares of outer radius R and inner radius r. Make a formula for this statement.

A man bought 25a articles at 30p paisa each and sold them at 20q paisa each. Find his profit in rupees.

How many minutes are there in x hours, y minutes and z seconds.

Apple cost x rupees per dozen and mangoes cost y rupees per score. Write a formula to find the total cost C in rupees of 20 apples and 30 mangoes.

Make R the subject of formula A = `"P"(1 + "R"/100)^"N"`

Make L the subject of formula T = `2pisqrt("L"/"G")`

Make a the subject of formula S = `"ut" + (1)/(2)"at"^2`

Make x the subject of formula `"a"x^2/"a"^2 + y^2/"b"^2` = 1

Make a the subject of formula S = `("a"("r"^"n" - 1))/("r" - 1)`

Make r₂ the subject of formula `(1)/"R" = (1)/"r"_1 + (1)/"r"_2`

Make a the subject of formula x = `sqrt(("a" + "b")/("a" - "b")`

Make y the subject of formula W = `"pq" + (1)/(2)"wy"^2`

Make N the subject of formula I = `"NG"/("R" + "Ny")`

Make V the subject of formula K = `(1)/(2)"MV"^2`

Make d the subject of formula S = `"n"/(2){2"a" + ("n" - 1)"d"}`

Make R₂ the subject of formula R² = 4π(R₁² - R₂²)

Make A the subject of formula R = `("m"_1"B" + "m"_2"A")/("m"_1 + "m"_2)`

Make c the subject of formula x = `(-"b" ± sqrt("b"^2 - 4"ac"))/(2"a")`

Make k the subject of formula T = `2pisqrt(("k"^2 + "h"^2)/"hg"`

Given: mx + ny = p and y = ax + b. Find x in terms of m, n, p, a and b.

If A =  pr² and C = 2pr, then express r in terms of A and C.

If V = pr²h and S = 2pr² + 2prh, then express V in terms of S, p and r.

If 3ax + 2b² = 3bx + 2a², then express x in terms of a and b. Also, express the result in the simplest form.

If b = `(2"a")/("a" - 2)`, and c = `(4"b" - 3)/(3"b" + 4)`, then express c in terms of a.

Make h the subject of the formula R = `"h"/(2)("a" - "b")`. Find h when R = 108, a = 16 and b = 12.

Make s the subject of the formula v² = u² + 2as. Find s when u = 3, a = 2 and v = 5.

Make y the subject of the formula x = `(1 - y^2)/(1 + y^2)`. Find y if x = `(3)/(5)`

Make a the subject of the formula S = `"n"/(2){2"a" + ("n" - 1)"d"}`. Find a when S = 50, n = 10 and d = 2.

Make x the subject of the formula a = `1 - (2"b")/("cx" - "b")`. Find x, when a = 5, b = 12 and 

Make h the subject of the formula K = `sqrt("hg"/"d"^2 - "a"^2`. Find h, when k = -2, a = -3, d = 8 and g = 32.

Make x the subject of the formula y = `(1 - x^2)/(1 + x^2)`. Find x, when y = `(1)/(2)`

Make y the subject of the formula `x/"a" + y/"b" `= 1. Find y, when a = 2, b = 8 and x = 5.

Make m the subject of the formula x = `"my"/(14 - "mt")`. Find m, when x = 6, y = 10 and t = 3.

Make I the subject of the following M = `"L" /"F"(1/2"N" - "C") xx "I"`. Find I, If M = 44, L = 20, F = 15, N = 50 and C = 13.

Make g the subject of the formula v² = u² - 2gh. Find g, when v = 9.8, u = 41.5 and h = 25.4.

Make f the subject of the formula D = `sqrt((("f" + "p")/("f" - "p"))`. Find f, when D = 13 and P = 21.

Make z the subject of the formula y = `(2z + 1)/(2z - 1)`. If x = `(y + 1)/(y - 1)`, express z in terms of x, and find its value when x = 34.

Make c the subject of the formula a = b(1 + ct). Find c, when a = 1100, b = 100 and t = 4.

"The volume of a cylinder V is equal to the product of π and square of radius r and the height h". Express this statement as a formula. Make r the subject formula. Find r, when V = 44cm³, π = `(22)/(7)`, h = 14cm.

"The volume of a cone V is equal to the product of one third of π and square of radius r of the base and the height h". Express this statement as a formula. Make r the subject formula. Find r, when V = 1232cm³, π = `(22)/(7)`, h = 24cm.

The pressure P and volume V of a gas are connected by the formula PV = C; where C is a constant. If P = 4 when V = `2(1)/(2)`; find the value of P when V = 4?

The total energy E possess by a body of Mass 'm', moving with a velocity 'v' at a height 'h' is given by: E = `(1)/(2) "m" "u"^2 + "mgh"`. Make 'm' the subject of formula.

The total energy E possess by a body of Mass 'm', moving with a velocity 'v' at a height 'h' is given by: E = `(1)/(2) "m" "u"^2 + "mgh"`. Find m, if v = 2, g = 10, h = 5 and E = 104.

If s = `"n"/(2)[2"a" + ("n" - 1)"d"]`, the n express d in terms of s, a and n. find d if n = 3, a = n + 1 and s = 18.

"Area A oof a circular ring formed by 2 concentric circles is equal to the product of pie and the difference of the square of the bigger radius R and the square of the bigger radius R and the square of the smaller radius r. Express the above statement as a formula. Make r the subject of the formula and find r, when A = 88 sq cm and R = 8cm.