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The difference in the age of two people is 24 years. If 6 years ago, the older of the two was four times as old as the younger one, then find their present ages.
15 and 39 years
12 and 36 years
14 and 38 years
16 and 40 years
14 and 38 years
Check the options by subtracting 6 from both numbers and verifying if the older is 4 times the younger. Option C: 38-6=32 and 14-6=8. Since 32 = 4 ├Ч 8, this matches.
Age difference = 24 years, 6 years ago age ratio was 4:1.
(xтИТ6)=4(yтИТ6)┬аand┬аxтИТy=24
Check the options by subtracting 6 from both numbers and verifying if the older is 4 times the younger. Option C: 38-6=32 and 14-6=8. Since 32 = 4 ├Ч 8, this matches.
Many students calculate 4 times the current age instead of the age 6 years ago, or confuse the difference by adding 6 to the wrong side of the equation.
Define Variables
Let the present age of the older person be x and the younger be y. We know xтИТy=24.
xтИТy=24
Set up Ratio Equation
Six years ago, their ages were (xтИТ6) and (yтИТ6). The older was 4 times the younger.
xтИТ6=4(yтИТ6)
Solve the System
Substitute x=y+24 into the ratio equation: (y+24)тИТ6=4yтИТ24. Simplifying, y+18=4yтИТ24.
3y=42тЯ╣y=14
Calculate Ages
If the younger is 14, then x=14+24=38.
x=38,y=14
C is correct because calculations yield ages of 38 and 14 years, which satisfy both the difference of 24 and the ratio condition.
Age problems are essentially systems of linear equations; always test the options for verification to save time in competitive exams.
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