Question

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?​

Answer 1

$\huge{\underline{\purple{\rm{Solution:}}}}$

$\small{\underline{\red{\rm{Given:}}}}$

• $\rm{Arvind\:paid=\dfrac{1}{2}\:of\:the\:sum\:of\:the\:other\:boys}$

• $\rm{Akash\:paid=\dfrac{1}{3}\:of\:the\:sum\:of\:the\:other\:boys}$

• $\rm{Suresh\:Paid=\dfrac{1}{4}\:of\:the\:sum\:of\:the\:other\:boys}$

$\small{\underline{\red{\rm{let:}}}}$

• $\rm{The\: amount\:paid\:by\: Jaggi\:be\:J}$
• $\rm{The\: other\:boys\:be\:x\:y\:z}$

$\small{\underline{\red{\rm{To\: Find:}}}}$

• Amount paid by Jaggi

$\rm{Now,\: calculate\: amount\:paid\:by\:x\:y\:z}$

$\rm{\implies Amount\:paid\:by\: Arvind}$

$\rm{\implies x=\dfrac{1}{2}(6000-x)}$

$\rm{\implies 2x=60000-x}$

$\rm{\implies 2x+x=60000}$

$\rm{\implies 3x=60000}$

$\rm\green{\implies x=20000}$

$\rm{\implies Amount\:paid\:by\: Akash}$

$\rm{\implies y=\dfrac{1}{3}(6000-y)}$

$\rm{\implies 3y=60000-y}$

$\rm{\implies 4y=60000}$

$\rm\green{\implies y=15000}$

$\rm{\implies Amount\:paid\:by\: Suresh}$

$\rm{\implies z=\dfrac{1}{4}(6000-z)}$

$\rm{\implies 4z=60000-z}$

$\rm{\implies 5z=60000}$

$\rm\green{\implies z=12000}$

$\rm{\implies Amount\:paid\:by\:Jaggi}$

$\rm{\implies Sum\:of\:x\:y\:z\:J=Total\: amount}$

$\rm{\implies 20000+15000+12000+J=60000}$

$\rm{\implies 47000+J=60000}$

$\rm{\implies J=60000-47000}$

$\rm{\implies J=13000}$

Hence,

$\rm\green{The\: amount\:paid\:by\: Jaggi=Rs.13000}$