Question : The students in three classes are in the ratio 4 : 6 : 9. If 12 students are increased in each class, the ratio changes to 7 : 9 : 12. Then, the total number of students in the three classes before the increase is:
Option 1: 95
Option 2: 76
Option 3: 100
Option 4: 114
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Correct Answer: 76
Solution : Given: The students in the three classes are in the ratio of 4 : 6 : 9. Let the original number of students be $4x,6x,$ and $9x$. According to the question, $\frac{4x+12}{6x+12}=\frac{7}{9}$ ⇒ $42x+84=36x+108$ ⇒ $6x=24$ $\therefore x=4$ So, the required number of students $=(4x+6x+9x)=19x=19×4=76$ Hence, the correct answer is 76.
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Question : A, B and C invested capital in the ratio 5 : 7 : 4, the timing of their investments being in the ratio x : y : z. If their profits are distributed in the ratio 45 : 42 : 28, then x : y : z =?
Option 1: 9 : 6 : 7
Option 2: 7 : 9 : 4
Option 3: 9 : 4 : 7
Option 4: 6 : 7 : 9
Question : Which of the following is the smallest ratio? $\frac{5}{6}, \frac{7}{9}, \frac{11}{12}, \frac{13}{18}$
Option 1: $\frac{7}{9}$
Option 2: $\frac{13}{18}$
Option 3: $\frac{5}{6}$
Option 4: $\frac{11}{12}$
Question : Directions: By Interchanging the given two numbers which of the following equations will be not correct? 7 and 4
Option 1: 8 ÷ 6 × 9 + 7 – 4 = 12
Option 2: 7 × 8 + 4 – 6 ÷ 3 = 37
Option 3: 9 – 4 × 3 + 6 × 7 ÷ 1 = 12
Option 4: 4 × 8 – 9 ÷ 3 + 7 = 57
Question : The radii of two cylinders are in the ratio 3 : 4 and their heights are in the ratio 8 : 5. The ratio of their volumes is equal to:
Option 1: 9 : 10
Option 2: 8 : 9
Option 3: 9 : 11
Option 4: 7 : 10
Question : The ratio of the monthly incomes of X and Y is 5 : 4 and that of their monthly expenditures is 9 : 7. If the income of Y is equal to the expenditure of X, then what is the ratio of the savings of X and Y?
Option 1: 9 : 8
Option 2: 6 : 7
Option 3: 8 : 9
Option 4: 7 : 6
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