Ratio and Proportion | Class 9 | Problem Set 4

Ratio and Proportion | Class 9 | Problem Set 4

Ratio and Proportion | Class 9 | Problem Set 4, miscellaneous examples of this problem set are solved and attached in a pdf file.

Problem-Set-4

The examples solved in this article are dependent on the following topics –

(1) Reducing the given numbers to the simple form and finding their ratio.

(2) Use of theorem of equal ratios.

(3) Use of operations like componendo, dividendo, invertendo and alternando.

(4) Continued proportion and solving examples based on it.

(5) Solving different equations to get their solution.

Also read : Ratio and Proportion | Class 9 | Practice Set 4.2

The following examples are solved here.

(1) Select the appropriate alternative answer for the following questions.
(i) If 6 : 5 = y : 20 then what will be the value of y ?
(A) 15 (B) 24 (C) 18 (D) 22.5

(ii) What is the ratio of 1 mm to 1 cm ?
(A) 1 : 100 (B) 10 : 1 (C) 1 : 10 (D) 100 : 1

(iii) The ages of Jatin, Nitin and Mohasin are 16, 24 and 36 years respectively. What is the ratio of Nitin’s age to Mohasin’s age ?
(A) 3 : 2 (B) 2 : 3 (C) 4 : 3 (D) 3 : 4

iv) 24 Bananas were distributed between Shubham and Anil in the ratio 3 : 5, then how many bananas did Shubham get ?
(A) 8 (B) 15 (C) 12 (D) 9

(v) What is the mean proportional of 4 and 25 ?
(A) 6 (B) 8 (C) 10 (D) 12

(2) For the following numbers write the ratio of first number to second number in the reduced
form.
(i) 21, 48 (ii) 36, 90 (iii) 65, 117 (iv) 138, 161 (v) 114, 133

(3) Write the following ratios in the reduced form.
(i) Radius to the diameter of a circle. (ii) The ratio of diagonal to the length of a rectangle, having length 4 cm and breadth 3 cm. (iii) The ratio of perimeter to area of a square, having side 4 cm.

(4) Check whether the following numbers are in continued proportion.
(i) 2, 4, 8 (ii) 1, 2, 3 (iii) 9, 12, 16 (iv) 3, 5, 8

(5) a, b, c are in continued proportion. If a = 3 and c = 27 then find b.

(6) Convert the following ratios into percentages..
(i) 37 : 500 (ii) 5 : 22

(7) Write the ratio of first quantity to second quantity in the reduced form.
(i) 1024 MB, 1.2 GB [(1024 MB = 1 GB)] (ii) 17 Rupees, 25 Rupees 60 paise (iii) 5 dozen, 120 units
(iv) 4 sq.m, 800 sq.cm (v) 1.5 kg, 2500 gm

Also read : Ratio and Proportion | Class 9 | Practice Set 4.3

(If a / b = 2 / 3, then find the values of the following expressions.

(9) If a, b, c, d are in proportion, then prove the following.

(10) If a, b, c are in continued proportion, then prove the following.

(11) Solve the given equation.