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 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 ?
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?
If (p + q) ∶ (q + r) ∶ (r + p) = 5 ∶ 6 ∶ 7 and p + q + r = 18, find the value of p ∶ q ∶ r
A bag contains Rs. 420 in the form of 5 rupee, 2 rupee, and 1 rupee coins. The number of coins of 5 rupee, 2 rupee, and 1 rupee is in the ratio of 2 : 3 : 5. What is the total number of coins in the bag?
