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
If x : y = 5 : 2, then the value of (8x + 9y) : (8x + 2y) is:
If the value of \(\frac{{p - q}}{q} = \frac{4}{3}\) .find p : q
Half of the villagers of a certain village have their own houses. One-fifth of the villagers cultivate paddy. One-third of the villagers are literate. Four-fifth of the villagers are under 25 years of age. Which one of the following statements is certainly correct ?
The two numbers are in the ratio of 9 ∶ 7 and the difference between of these two number is 6000. What is the sum of the two numbers?
A certain number is added to each of a pair of numbers which are in the ratio 4 ∶ 5. The sum of the resulting numbers is 39 and their ratio (taken in the same order as mentioned above) is 6 ∶ 7. What is the number added?
