(English Medium) ICSE Class 10 - CISCE Question Bank Solutions for Mathematics

If the ratio between 8 and 11 is the same as the ratio of 2x - y to x + 2y, find the value of `(7"x")/(9"y")`

Divide Rs 1,290 into A, B and C such that A is `2/5` of B and B : C = 4 : 3.

A school has 630 students. The ratio of the number of boys to the number of girls is 3 : 2. This ratio changes to 7 : 5 after the admission of 90 new students. Find the number of newly admitted boys.

In a mixture of 126 kg of milk and water, milk and water are in ratio 5 : 2. How much water must be added to the mixture to make this ratio 3 : 2?

If 2a = 3b and 4b = 5c, find: a : c.

If (x + 3) : (4x + 1) is the duplicate ratio of 3 : 5, find the value of x. 

If (3x - 9) : (5x + 4) is the triplicate ratio of 3 : 4, find the value of x. 

If r² ₌pq, show that p : q is the duplicate ratio of (p + r) : (q + r).

If (p - x) : (q - x) be the duplicate ratio of p : q then show that: `1/"p" + 1/"q" = 1/"x"`

If x², 4 and 9 are in continued proportion, find x.

If a,b,c are in continued proportion,
show that: `("a"^2 + "b"^2)/("b"("a" + "c")` = `("b"("a" + "c"))/("b"^2 + "c"^2)`

If `"a"/"b" = "c"/"d"`, show that: `(a^3c + ac^3)/(b^3d + bd^3) = ("a" + "c")^4/("b" + "d")^4`

A woman reduces her weight in the ratio 7 : 5. What does her weight become if originally it was 84 kg?

If x and y both are positive and (2x² – 5y²) : xy = 1 : 3, find x : y.

If `(7"m" + 2"n")/(7"m" - 2"n") = 5/3` use properties of proportion to find:

(i) m : n

(ii) `("m"^2 + "n"^2)/("m"^2 - "n"^2)`

If b is the mean proportion between a and c, show that: 

`("a"^4 + "a"^2"b"^2   + "b"^4)/("b"^4 + "b"^2"c"^2   +"c"^4) = "a"^2/"c"^2`

If `x/a = y/b = z/c` show that: `x^3/a^3 + y^3/b^3 + z^3/c^3 = (3xyz)/(abc)`.

Given `(x^3 + 12x)/(6x^2 + 8) = (y^3 + 27y)/(9y^2 + 27)`. Using componendo and dividendo, find x : y.

Draw two concentric circles with radii 4 cm and 6 cm. Taking a point on the outer circle, construct a pair of tangents to inner circle. By measuring the lengths of both the tangents, show that they are equal to each other.

There is a continuous growth in population of a village at the rate of 5% per annum. If its present population is 9,261, what population was 3 years ago?