1b:["$","section",null,{"className":"mt-8","children":[["$","h2",null,{"className":"border-b pb-2 text-xl font-bold","children":"Answer & solution"}],["$","ul",null,{"className":"mt-4 space-y-2","children":[["$","li","33011",{"className":"flex items-start gap-3 rounded-xl border p-3 border-emerald-500 bg-emerald-500/10","children":[["$","span",null,{"className":"flex h-[1.806rem] shrink-0 items-center","children":["$","span",null,{"className":"grid h-6 w-6 place-items-center rounded-full border text-xs font-bold border-emerald-500 bg-emerald-500 text-white","children":["$","svg",null,{"ref":"$undefined","xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","stroke":"currentColor","strokeWidth":2,"strokeLinecap":"round","strokeLinejoin":"round","className":"lucide lucide-check h-3.5 w-3.5","children":[["$","path","1gmf2c",{"d":"M20 6 9 17l-5-5"}],"$undefined"]}]}]}],["$","div",null,{"className":"min-w-0 flex-1","children":[["$","div",null,{"suppressHydrationWarning":true,"className":"rte-render text-sm","dangerouslySetInnerHTML":{"__html":"

105 km

"}}],null]}]]}],["$","li","33012",{"className":"flex items-start gap-3 rounded-xl border p-3 ","children":[["$","span",null,{"className":"flex h-[1.806rem] shrink-0 items-center","children":["$","span",null,{"className":"grid h-6 w-6 place-items-center rounded-full border text-xs font-bold ","children":"B"}]}],["$","div",null,{"className":"min-w-0 flex-1","children":[["$","div",null,{"suppressHydrationWarning":true,"className":"rte-render text-sm","dangerouslySetInnerHTML":{"__html":"

150 km

"}}],null]}]]}],["$","li","33013",{"className":"flex items-start gap-3 rounded-xl border p-3 ","children":[["$","span",null,{"className":"flex h-[1.806rem] shrink-0 items-center","children":["$","span",null,{"className":"grid h-6 w-6 place-items-center rounded-full border text-xs font-bold ","children":"C"}]}],["$","div",null,{"className":"min-w-0 flex-1","children":[["$","div",null,{"suppressHydrationWarning":true,"className":"rte-render text-sm","dangerouslySetInnerHTML":{"__html":"

130 km

"}}],null]}]]}],["$","li","33014",{"className":"flex items-start gap-3 rounded-xl border p-3 ","children":[["$","span",null,{"className":"flex h-[1.806rem] shrink-0 items-center","children":["$","span",null,{"className":"grid h-6 w-6 place-items-center rounded-full border text-xs font-bold ","children":"D"}]}],["$","div",null,{"className":"min-w-0 flex-1","children":[["$","div",null,{"suppressHydrationWarning":true,"className":"rte-render text-sm","dangerouslySetInnerHTML":{"__html":"

Cannot be determined

"}}],null]}]]}]]}],null,["$","div",null,{"className":"mt-4 rounded-xl border bg-muted/20 p-4","children":[["$","div",null,{"className":"mb-1 text-xs font-semibold uppercase tracking-wide text-muted-foreground","children":"Solution"}],["$","div",null,{"suppressHydrationWarning":true,"className":"rte-render text-sm","dangerouslySetInnerHTML":{"__html":"

Now, since X and Y reach C at the same time, $\frac{100 + B C}{64.875} = \frac{A C}{49.5},$ Hence, you need to take help from options. i.e.
\r\nIf AC = 105, BC² = AC² – AB² = 105² – 100² = 1025 or BC = 32
\r\nSo, $\frac{100 + B C}{A C} = \frac{132}{105} = 1.25$

"}}]]}]]}]

CAT 1999 — QA Question 41

Answer & solution