Question : If $x$ is subtracted from each of the numbers 20, 37, 54 and 105, then the numbers so obtained in this order are in proportion. What is the mean proportional between $(7 x-5)$ and $(x+1) $?
Option 1: 8
Option 2: 9
Option 3: 6
Option 4: 12
Correct Answer: 8
Solution : If $x$ is subtracted from each of the numbers 20, 37, 54 and 105, then the numbers so obtained in this order are in proportion. So, $\frac{(20-x)}{(37-x)} = \frac{(54-x)}{(105-x)}$ $⇒[(20-x)(105-x)]=[(54-x)(37-x)]$ $⇒34x=102$ $⇒x = 3$ The mean proportional between $(7x-5)$ and $(x+1)$ is the square root of their product. So, the mean proportional is $\sqrt{(7x-5)(x+1)}$. Substituting $x = 3$ into the above expression, we get $\sqrt{(7\times3-5)(3+1)} = \sqrt{(16)(4)} = 8$ Hence, the correct answer is 8.
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Question : How many numbers between 400 and 700 are divisible by 5, 6 and 7?
Question : How many numbers between 300 and 700 are divisible by 5, 6, and 8?
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?
Question : The ratio of the third proportional to 16 & 40 and the mean proportional between 10 & 40 is:
Question : If $x^2-3 x+1=0$, then the value of $\left(x^4+\frac{1}{x^2}\right) \div\left(x^2+1\right)$ is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile