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Two numbers are in the ratio 2 : 4. If the first number is increased by 4 and the second number is decreased by 14, then the ratio becomes 8 : 5. What is the sum of the original two numbers?
41
24
38
36
36
Use the cross-multiplication method: 2(5) - 4(8) = 10 - 32 = -22 units difference. Then, 4(5) - (-14)(8) = 20 + 112 = 132. So, 22 units = 132, 1 unit = 6.
Two numbers are in the ratio 2 : 4. First number + 4, second number - 14 leads to the ratio 8 : 5.
4xтИТ142x+4тАЛ=58тАЛ
Use the cross-multiplication method: 2(5) - 4(8) = 10 - 32 = -22 units difference. Then, 4(5) - (-14)(8) = 20 + 112 = 132. So, 22 units = 132, 1 unit = 6.
Students often misinterpret the order of operations by adding/subtracting in the wrong numerator or denominator or confusing the ratio variables.
Define variables based on ratio
Let the first number be 2x and the second number be 4x.
2x,4x
Set up the equation
According to the problem, (2x+4)/(4xтИТ14)=8/5.
4xтИТ142x+4тАЛ=58тАЛ
Solve for x
Cross-multiply to get 5(2x+4)=8(4xтИТ14), which simplifies to 10x+20=32xтИТ112. Rearranging gives 22x=132, so x=6.
x=6
Calculate the sum
The original sum is 2x+4x=6x. Substituting x=6, we get 6├Ч6=36.
Sum=6├Ч6=36
D is correct because the calculated value of the sum of the two numbers is 36.
This concept of varying ratios is foundational for 'Mixture and Alligation' problems commonly found in banking and SSC exams.
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