Ratio Between Two Numbers and Their Sum
दो संख्याओं का अनुपात 19 : 24 है। यदि प्रत्येक संख्या में से 36 घटा दिया जाए, तो अनुपात 3 : 4 हो जाता है। संख्याओं का योग ज्ञात कीजिए।
The ratio between two numbers is 19 : 24. If each number is reduced by 36, the ratio becomes 3 : 4. Find the sum of the numbers.
Solution (समाधान):
Let the two numbers be 19x and 24x.
After subtracting 36 from each number, the new ratio is given as:
(19x − 36) ÷ (24x − 36) = 3 ÷ 4
Step-by-step calculation:
- Cross multiply to eliminate the fraction:
- 4 × (19x − 36) = 3 × (24x − 36)
- Expanding both sides: 76x − 144 = 72x − 108
- Bring like terms together: 76x − 72x = 144 − 108
- 4x = 36
- Divide both sides by 4: x = 9
Find the original numbers:
- First number = 19 × 9 = 171
- Second number = 24 × 9 = 216
Sum of the numbers:
171 + 216 = 387
Final Answer: 387
Quick Revision / Key Points:
- Represent numbers in terms of a variable using the given ratio.
- Apply the condition after reducing each number by 36 to form an equation.
- Use cross multiplication to solve the equation.
- Calculate the value of the variable and then find the original numbers.
- Sum the original numbers to get the final answer.