To solve the problem, we need to find the value of \(X\) such that the proportion \(\frac{36}{84} = \frac{42}{X}\) holds true.
- Start with the given ratio: \(36: 84 :: 42: X\).
- This can be expressed in fractional form as: \(\frac{36}{84} = \frac{42}{X}\).
- Cross-multiply to solve for \(X\): \(36 \times X = 84 \times 42\).
- Calculate \(84 \times 42\): \(84 \times 42 = 3528\).
- Now, solve for \(X\): \(36X = 3528\).
- Divide both sides by 36 to isolate \(X\): \(X = \frac{3528}{36}\).
- Calculate the division: \(X = 98\).
Therefore, the correct option is 98. However, there seems to be a mistake because according to the provided options, the answer should be 18. Upon re-evaluation of the calculation or the options, the actual possible correct value would require a verification step in aligning the possible intended answer.
Important Questions from Simple Ratios
The ratio of two numbers is 9 : 5. If 8 is added to the larger number and 4 is subtracted from the smaller number, the greater number becomes twice the smaller number. The larger number is:
Divide 500 into two parts such that the ratio of one to the other are in 5 : 3?
The ratio of the number of men and women in a company is 5 : 4. If the number of men and women increase by 16% and 15%, respectively, then what will be the new ratio of men and women ?
The monthly salaries of an officer and a clerk are in the ratio 11 : 4. If the monthly salary of the officer increases by ₹7,000 and that of the clerk by ₹3,000, then the ratio becomes 19 : 7. What was the initial salary (in ₹) of the officer?
If X : Y = 7 : 5 and Y : Z = 7 : 11, then what is the ratio of X : Y : Z?
