Arvind, Akash, Sunil and Jaggi bought a motorbike for Rs. 60000. Arvind paid one-half of the sum of the amounts paid by the other other boys, Aakash paid one-third of the sum of the amounts paid by the other boys; and Suresh paid of one-fourth of the sum of the amounts paid by the other boys. How much did Jaggi has to pay?
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Arvind, Akash, Sunil and Jaggi bought a motorbike for Rs. 60000. Arvind paid one-half of the sum of the amounts
[tex]\huge{\underline{\purple{\rm{Solution:}}}}[/tex]
[tex]\small{\underline{\red{\rm{Given:}}}}[/tex]
[tex]\small{\underline{\red{\rm{let:}}}}[/tex]
[tex]\small{\underline{\red{\rm{To\: Find:}}}}[/tex]
[tex]\rm{Now,\: calculate\: amount\:paid\:by\:x\:y\:z}[/tex]
[tex]\rm{\implies Amount\:paid\:by\: Arvind}[/tex]
[tex]\rm{\implies x=\dfrac{1}{2}(6000-x)}[/tex]
[tex]\rm{\implies 2x=60000-x}[/tex]
[tex]\rm{\implies 2x+x=60000}[/tex]
[tex]\rm{\implies 3x=60000}[/tex]
[tex]\rm\green{\implies x=20000}[/tex]
[tex]\rm{\implies Amount\:paid\:by\: Akash}[/tex]
[tex]\rm{\implies y=\dfrac{1}{3}(6000-y)}[/tex]
[tex]\rm{\implies 3y=60000-y}[/tex]
[tex]\rm{\implies 4y=60000}[/tex]
[tex]\rm\green{\implies y=15000}[/tex]
[tex]\rm{\implies Amount\:paid\:by\: Suresh}[/tex]
[tex]\rm{\implies z=\dfrac{1}{4}(6000-z)}[/tex]
[tex]\rm{\implies 4z=60000-z}[/tex]
[tex]\rm{\implies 5z=60000}[/tex]
[tex]\rm\green{\implies z=12000}[/tex]
[tex]\rm{\implies Amount\:paid\:by\:Jaggi}[/tex]
[tex]\rm{\implies Sum\:of\:x\:y\:z\:J=Total\: amount}[/tex]
[tex]\rm{\implies 20000+15000+12000+J=60000}[/tex]
[tex]\rm{\implies 47000+J=60000}[/tex]
[tex]\rm{\implies J=60000-47000}[/tex]
[tex]\rm{\implies J=13000}[/tex]
Hence,
[tex]\rm\green{The\: amount\:paid\:by\: Jaggi=Rs.13000}[/tex]