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

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?

The population of a town 2 years ago was 62,500. Due to migration to cities, it decreases at the rate of 4% per annum. Find its present population.

The total number of industries in a particular portion of the country is approximately 1,600. If the government has decided to increase the number of industries in the area by 20% every year; find the approximate number of industries after 2 years.

6000 workers were employed to construct a river bridge in four years. At the end of first year, 20% workers were retrenched; At the end of second year 5% of the workers at that time were retrenched. However, to complete the project in time, the number of workers was increased by 15% at the end of third year. How many workers were working during the fourth year?

Mr. Kumar borrowed Rs. 15,000 for two years. The rate of interest for the two successive years are 8% and 10% respectively. If he repays Rs. 6,200 at the end of the first year, find the outstanding amount at the end of the second year.

The compound interest, calculated yearly, on a certain sum of money for the second year is Rs. 1320 and for the third year is Rs. 1452. Calculate the rate of interest and the original sum of money.