Let's solve the given problem step-by-step.
The problem provides us with the relation: \(a:3 = b:7 = c:9\). This indicates that \(a\), \(b\), and \(c\) are proportional to 3, 7, and 9, respectively.
We start by expressing \(a\), \(b\), and \(c\) in terms of a common variable \(k\):
- \(a = 3k\)
- \(b = 7k\)
- \(c = 9k\)
Now, we need to find the value of \(\frac{a+b+c}{a}\). Using the values above:
Substitute \(a\), \(b\), and \(c\):
- \(a + b + c = 3k + 7k + 9k = 19k\)
- \(a = 3k\)
Now, calculate \(\frac{a+b+c}{a}\):
\(\frac{a+b+c}{a} = \frac{19k}{3k}\)
Simplify the expression:
\(\frac{19k}{3k} = \frac{19}{3}\)
Therefore, the correct answer is \(\frac{19}{3}\).
This matches the given option:
\(\frac{19}{3}\)
Thus, the answer is option \(\frac{19}{3}\).
Similar Questions
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- If $a : b :: 3 : 4$ then the value of the expression $\frac{5a - 3b}{7a + 2b}$ is:
- If the third proportional of 8 and 20 be x, then what is the value of x?
- If $0.75 : x :: 25 : 8$, then what is the value of $x$?
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- If $\frac{A}{4} = \frac{B}{5} = \frac{C}{6}$, then $A : B : C$ is:
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Important Questions from Ratio and Proportion
In a mixture of 156 litres, the ratio of milk and water is 7 : 6. How much water should be added to make the ratio 14 : 13?
If the ratio of the first to second number is 3 : 4 and that of the second to the third number is 8 : 5, and sum of three numbers is 190 then the third number is:
The third proportional to 9 and 15 is:
The average age of 3 persons is 30 years.If their ages are in the ratio of 3 : 5 : 7 respectively, then the age of the eldest person is:
The income of A and B are in the ratio 5 : 3. The expenses of A, B and C are in the ratio of 8 : 5 : 2. If C spends 2000 and B saves ₹ 700, then A saves:
