Ratio and Proportion Questions and Answers Quiz 1

Ratio and Proportion Questions and Answers Quiz 1

1 . A bag contains 50 p, 25 p and 10 p coins in the ratio 5 : 9 : 4, amounting to Rs.206. Find the number of coins of each type respectively. A.   200, 305, 106 B.   210, 350, 148 C.   200, 360, 160 D.   200, 160, 180 2 . The ratio of length to width of a rectangular sheet of paper is 5 : 3. If the width of the sheet is 18 cm, find its length? A.   10 cm B.   20 cm C.   25 cm D.   30 cm 3 . The ratio between the number of men and women in an office is 5 : 7. If the number of women working in the office is 56. Find the number of men working in the office? A.   40 B.   50 C.   45 D.   60 4 . If (a + b) : (a - b) = 15 : 1, then the value of $a^ 2$ - $b^ 2$ is : A.   56 B.   15 C.   112 D.   8 5 . The students in three classes are in the ratio of 2 : 3 : 4. If 40 students are added in each class, the ratio becomes 4 : 5 : 6. Find the total number of students in all the three classes is : A.   270 B.   180 C.   126 D.   135 6 . Two equal containers are filled with the mixture of milk and water. The concentration of milk in each of the container is 20% and 25% respectively. What is the ratio of water in both the containers respectively? A.   15:16 B.   16:15 C.   4:5 D.   5:4 7 . A camel pursue an elephant and takes 5 leaps for every 7 leaps of the elephant, but 5 leaps of elephant are equal to 3 leaps of camel. What is the ratio of speeds of camel and elephant? A.   21:25 B.   24:23 C.   25:21 D.   23:24 8 . The age of Sachin is 4 times that of his son. Five years ago Sachin was nine times as old as his son was at that time. The present age of the Sachin is : A.   25 years B.   36 years C.   32 years D.   48 years 9 . Bhanu and Shafeeq started a business by investing Rs.36,000 and Rs.63,000. Find the share of each respectively, out of an annual profit of Rs.5500. A.   2000,5500 B.   2500,4500 C.   3000,4000 D.   2000,3500 10 . If A : B = 3 : 4 and B : C = 8 : 9, then A : C is : A.   1:3 B.   3:2 C.   2:3 D.   1:2

Answers & Solutions   1 .     Answer : Option C Explanation : Let the number of 50 p, 25 p and 10 p coins be 5x, 9x and 4x respectively. Then, $5x\over2$+$9x\over4$+$4x\over10$ = 206 $50x+45x+8x=4120$ $103x=4120$ $x=40$ Number of 50 p coins = (5 × 40) = 200; number of 25 p coins = (9 × 40) = 360; number of 10 p coins = (4 × 40) = 160 2 .     Answer : Option D Explanation : Let the length of sheet of paper be x cm. Then the ratio of length to width = x : 18 Thus, x : 18 = 5 : 3 x × 3 = 18 × 5 x = 30 Hence the length of paper = 30 cm 3 .     Answer : Option A Explanation : 5 : 7 = x : 56 (suppose number of men = x) x = 40 (by the first property) Therefore, number of men in the office = 40 4 .     Answer : Option B Explanation : $(a+b)\over(a-b)$=$15\over1$ $a\over b$ = $8\over7$ (by compnendo and dividend) Therefore, $a^ 2$ - $b^ 2$ = 64-49 = 15 5 .     Answer : Option B Explanation : 2x + 40 = 4y … (i) 3x + 40 = 5y …. (ii) 4x + 40 = 6y ….. (iii) Therefore 2x = 40 x = 20 Hence, total number of students = 2x + 3x + 4x = 9x = 9 × 20 = 180 6 .     Answer : Option B Explanation : Milk $\,\,\,\,\,$ 20% $\,\,\,\,\,$ 25% Water $\,\,\,$ 80% $\,\,\,\,$ 75% Therefore, required ratio =$80\over75$=$16\over15$ or 16:15 7 .     Answer : Option C Explanation : Ratio of speed of camel and elephant = $5\over3$:$7\over5$=$5\over3\times$15:$7\over5\times$15=25:21 8 .     Answer : Option C Explanation : Let the age of son is x years, then the age of Sachin will be 4x years. So, (4x - 5) = 9 (x - 5) | x = 8 So, age of Sachin is 32 years. 9 .     Answer : Option D Explanation : Ratio of shares of Bhanu and Shafeeq = 36000 : 63000 = 4 : 7 So, Share of Bhanu = 5500 × $4\over11$ = Rs.2000 And share of Shafeeq = 5500 x $7\over11$ = Rs.3500 10 .     Answer : Option C Explanation : [$A\over B$ = $3\over 4$, $B\over C$=$8\over 9$] $A\over C$= [$A\over B$$\times$$B\over C$] = [$3\over 4$$\times$$8\over 9$] =$2\over 3$ A:C = 2:3