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The government recently started a special train to connect the remote areas with the main cities. The basic one-way fare for a child between $3$ and $10$ years costs half the regular fare for an adult plus a reservation charge that is the same on the child's ticket as on the adulťs ticket. One reserved ticket for an adult costs $\$216$ and the cost of a reserved ticket for an adult and a child (aged between $3$ and $10$) costs $\$327$. What is the basic fare for the journey for an adult ?

  1. $\$111$
  2. $\$52.5$
  3. $\$210$
  4. $\$58.5$
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Option C. $210

Let reservation charge be x  [common for adult and child]

Reserved ticket for an child costs \$111     [ i.e. \$327 – $216 ]

Basic fare of Child,  $\frac{\$216 - x}{2}$ = $111 – x   [ costs half the regular fare for an adult ]

gives x = $6

therefore, Basic fare of Adult = Cost of reserved ticket – Reservation charge

                                              =  \$216 – $6 = $210

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