1.

X and Y are two natural numbers. The sum of thrice of X and twice of Y is 230. If 3X increases by 40% and 2Y increases by 30% then their sum will increase by 84. If X decreases by 40% and Y decreases by 30% then their sum will be `"______"`A. `58`B. `66`C. `52`D. `46`

Answer» Correct Answer - A
3x +2Y =230
If 3X increases by 40% and 2X increases by 30% total increase `=(40)/(100)(3X) +(30)/(100)(2Y)`
`:. (40)/(100) (3X) =(30)/(100)(2Y) =84`
`1x2X +0.6Y=84`
Dividing both sides by 0.6 ,2X +Y=140
`:. Y =40 -2X`
`:. 2Y =280 -4X`
`(1) rArr 2Y=230 -3X`
`:. 280 -4X =230 -3X`
`50=X`
`(2) rArr y=40`
The required sum `=X (1-(40)/(100)) +Y (1-(30)/(100))`
`=(50)(0.6) +(40)`
`=(0.7) =58`


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