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 A and B is 5 : 8. If 5 is added to each of A and B, then the ratio of A and B becomes 2 : 3. The sum of A and B is:
The ratio of two numbers A and B is 5: 8. If 5 is added to each of A and B, then the ratio becomes 2 : 3. The difference between A and B is:
A sum of Rs. 6342 is divided amongst A, B, C and D in the ratio 3 : 4 : 8 : 6. What is the difference between the shares of B and D?
The ratio of monthly incomes of A and B is 4 ∶ 5 and that of their monthly expenditures is 3 ∶ 8. If the income of A is equal to the expenditure of B, then what is the ratio of savings of A and B?
The ratio of the monthly incomes of A and B is 11 : 13 and the ratio of their expenditures is 9 : 11. If both of them manage to save Rs. 4,000 per month, then find the difference in their incomes (in Rs.)
