Question : Three numbers are in the ratio 5 : 6 : 7. If the product of the number is 5670, then the greatest number is:
Option 1: 15
Option 2: 18
Option 3: 21
Option 4: 28
Correct Answer: 21
Solution : Given: Three numbers are in the ratio 5 : 6 : 7. Let the numbers be $5x,6x,$ and $7x$, respectively. The product of the number is 5670. According to the question, $5x×6x×7x = 5670$ ⇒ $x^{3}=\frac{5670}{5×6×7}$ ⇒ $x^{3} = 27$ $\therefore x = 3$ $\therefore$ The greatest number $=7x = 7 ×3= 21$ Hence, the correct answer is 21.
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Question : The ratio between the two numbers is 3 : 4. If each number is increased by 6, the ratio becomes 4 : 5. What is the difference of the numbers?
Option 1: 1
Option 2: 3
Option 3: 6
Option 4: 8
Question : The time taken to travel the same distance by three cars is in the ratio of 12:15:10. What is the ratio of the speeds of the three cars?
Option 1: 4 : 5 : 6
Option 2: 4 : 6 : 5
Option 3: 5 : 4 : 6
Option 4: 5 : 6 : 4
Question : The ratio of two numbers is 4 : 5. If both numbers are increased by 4 the ratio becomes 5 : 6. What is the sum of the two numbers?
Option 1: 9
Option 3: 27
Option 4: 36
Question : If the product of three consecutive numbers is 210, then the sum of the smaller number is:
Option 1: 3
Option 2: 5
Option 3: 4
Option 4: 11
Question : If three numbers are in the ratio of 1 : 3 : 7, and their LCM is 336, then their HCF is:
Option 1: 16
Option 3: 10
Option 4: 12
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