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Question
The ages of A and B are in the ratio 3:1 . Fifteen years hence , the ratio will be 2:1 . Their present ages are :
30 years , 10 years
45 years , 15 years
21 years , 7 years
60 years , 20 years
ANSWER : 2
Descrption
<p><span style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; font - size: 18px; font - family: Karla; letter - spacing: - 0.36px; line - height: 25.2px; background: #ffffff;">Let the ages of A and B be 3x and x, respectively. Then</span><br style = "box - sizing: border - box; font - family: Karla; font - size: 18px; letter - spacing: - 0.36px; line - height: 25.2px; background - color: #ffffff;" /><br style = "box - sizing: border - box; font - family: Karla; font - size: 18px; letter - spacing: - 0.36px; line - height: 25.2px; background - color: #ffffff;" /><span style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; font - size: 18px; font - family: Karla; letter - spacing: - 0.36px; line - height: 25.2px; background: #ffffff;"><span class = "katex" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; font - size: 1em; font - weight: inherit; font - stretch: normal; font - family: KaTeX_Main, 'Times New Roman', serif; line - height: inherit; text - rendering: auto; position: relative; background: transparent;"><span class = "katex - html" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;" aria - hidden = "true"><span class = "base" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: relative; display: inline - block; white - space: nowrap; width: min - content; background: transparent;"><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;"><span class = "mfrac" style = "box - sizing: border - box; margin: 4px 0px; padding: 0px; border: 0px; outline: 0px; position: relative; display: inline - block; background: transparent;"><span class = "vlist - t vlist - t2" style = "box - sizing: border - box; margin: 0px - 2px 0px 0px; padding: 0px; border: 0px; outline: 0px; position: static; display: inline - table; table - layout: fixed; border - collapse: collapse; background: transparent;"><span class = "vlist - r" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; display: table - row; text - align: center; background: transparent;"><span class = "vlist" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: relative; display: table - cell; vertical - align: bottom; height: 1.32144em; background: transparent;"><span style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: relative; display: block; height: 0px; top: - 2.314em; background: transparent;"><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; display: inline - block; background: transparent;"><span class = "mord mathdefault" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; font - family: KaTeX_Math; font - style: italic; background: transparent;">x</span><span class = "mbin" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;"> + </span><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">1</span><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">5</span></span></span><span style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: relative; display: block; height: 0px; top: - 3.677em; background: transparent;"><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; display: inline - block; background: transparent;"><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">3</span><span class = "mord mathdefault" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; font - family: KaTeX_Math; font - style: italic; background: transparent;">x</span><span class = "mbin" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;"> + </span><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">1</span><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">5</span></span></span></span><span class = "vlist - s" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; font - size: 1px; position: static; display: table - cell; vertical - align: bottom; width: 2px; min - width: 2px; background: transparent;"></span></span></span></span></span><span class = "mrel" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;"> = </span></span><span class = "base" style = "box - sizing: border - box; margin: 0px 0px 3px; padding: 0px; border: 0px; outline: 0px; position: relative; display: inline - block; white - space: nowrap; width: min - content; background: transparent;"><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;"><span class = "mfrac" style = "box - sizing: border - box; margin: 4px 0px; padding: 0px; border: 0px; outline: 0px; position: relative; display: inline - block; background: transparent;"><span class = "vlist - t vlist - t2" style = "box - sizing: border - box; margin: 0px - 2px 0px 0px; padding: 0px; border: 0px; outline: 0px; position: static; display: inline - table; table - layout: fixed; border - collapse: collapse; background: transparent;"><span class = "vlist - r" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; display: table - row; text - align: center; background: transparent;"><span class = "vlist" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: relative; display: table - cell; vertical - align: bottom; height: 1.32144em; background: transparent;"><span style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: relative; display: block; height: 0px; top: - 2.314em; background: transparent;"><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; display: inline - block; background: transparent;"><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">1</span></span></span><span style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: relative; display: block; height: 0px; top: - 3.677em; background: transparent;"><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; display: inline - block; background: transparent;"><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">2</span></span></span></span><span class = "vlist - s" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; font - size: 1px; position: static; display: table - cell; vertical - align: bottom; width: 2px; min - width: 2px; background: transparent;"></span></span></span></span></span></span></span></span></span><br style = "box - sizing: border - box; font - family: Karla; font - size: 18px; letter - spacing: - 0.36px; line - height: 25.2px; background - color: #ffffff;" /><br style = "box - sizing: border - box; font - family: Karla; font - size: 18px; letter - spacing: - 0.36px; line - height: 25.2px; background - color: #ffffff;" /><span style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; font - size: 18px; font - family: Karla; letter - spacing: - 0.36px; line - height: 25.2px; background: #ffffff;">or <span class = "katex" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; font - size: 1em; font - weight: inherit; font - stretch: normal; font - family: KaTeX_Main, 'Times New Roman', serif; line - height: inherit; text - rendering: auto; position: relative; background: transparent;"><span class = "katex - html" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;" aria - hidden = "true"><span class = "base" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: relative; display: inline - block; white - space: nowrap; width: min - content; background: transparent;"><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">3</span><span class = "mord mathdefault" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; font - family: KaTeX_Math; font - style: italic; background: transparent;">x</span><span class = "mbin" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;"> + </span></span><span class = "base" style = "box - sizing: border - box; margin: 0px 0px 3px; padding: 0px; border: 0px; outline: 0px; position: relative; display: inline - block; white - space: nowrap; width: min - content; background: transparent;"><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">1</span><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">5</span><span class = "mrel" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;"> = </span></span><span class = "base" style = "box - sizing: border - box; margin: 0px 0px 3px; padding: 0px; border: 0px; outline: 0px; position: relative; display: inline - block; white - space: nowrap; width: min - content; background: transparent;"><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">2</span><span class = "mord mathdefault" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; font - family: KaTeX_Math; font - style: italic; background: transparent;">x</span><span class = "mbin" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;"> + </span></span><span class = "base" style = "box - sizing: border - box; margin: 0px 0px 3px; padding: 0px; border: 0px; outline: 0px; position: relative; display: inline - block; white - space: nowrap; width: min - content; background: transparent;"><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">3</span><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">0</span><span class = "mrel" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">⟹</span></span><span class = "base" style = "box - sizing: border - box; margin: 0px 0px 3px; padding: 0px; border: 0px; outline: 0px; position: relative; display: inline - block; white - space: nowrap; width: min - content; background: transparent;"><span class = "mord mathdefault" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; font - family: KaTeX_Math; font - style: italic; background: transparent;">x</span><span class = "mrel" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;"> = </span></span><span class = "base" style = "box - sizing: border - box; margin: 0px 0px 3px; padding: 0px; border: 0px; outline: 0px; position: relative; display: inline - block; white - space: nowrap; width: min - content; background: transparent;"><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">1</span><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">5</span></span></span></span></span><br style = "box - sizing: border - box; font - family: Karla; font - size: 18px; letter - spacing: - 0.36px; line - height: 25.2px; background - color: #ffffff;" /><span style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; font - size: 18px; font - family: Karla; letter - spacing: - 0.36px; line - height: 25.2px; background: #ffffff;"><span class = "katex" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; font - size: 1em; font - weight: inherit; font - stretch: normal; font - family: KaTeX_Main, 'Times New Roman', serif; line - height: inherit; text - rendering: auto; position: relative; background: transparent;"><span class = "katex - html" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;" aria - hidden = "true"><span class = "base" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: relative; display: inline - block; white - space: nowrap; width: min - content; background: transparent;"><span class = "mrel amsrm" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; font - family: KaTeX_AMS; background: transparent;">∴</span></span></span></span> A's age <span class = "katex" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; font - size: 1em; font - weight: inherit; font - stretch: normal; font - family: KaTeX_Main, 'Times New Roman', serif; line - height: inherit; text - rendering: auto; position: relative; background: transparent;"><span class = "katex - html" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;" aria - hidden = "true"><span class = "base" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: relative; display: inline - block; white - space: nowrap; width: min - content; background: transparent;"><span class = "mrel" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;"> = </span></span><span class = "base" style = "box - sizing: border - box; margin: 0px 0px 3px; padding: 0px; border: 0px; outline: 0px; position: relative; display: inline - block; white - space: nowrap; width: min - content; background: transparent;"><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">3</span><span class = "mbin" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">×</span></span><span class = "base" style = "box - sizing: border - box; margin: 0px 0px 3px; padding: 0px; border: 0px; outline: 0px; position: relative; display: inline - block; white - space: nowrap; width: min - content; background: transparent;"><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">1</span><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">5</span><span class = "mrel" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;"> = </span></span><span class = "base" style = "box - sizing: border - box; margin: 0px 0px 3px; padding: 0px; border: 0px; outline: 0px; position: relative; display: inline - block; white - space: nowrap; width: min - content; background: transparent;"><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">4</span><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">5</span><span class = "mord mathdefault" style = "box - sizing: border - box; margin: 0px 0.03588em 0px 0px; padding: 0px; border: 0px; outline: 0px; position: static; font - family: KaTeX_Math; font - style: italic; background: transparent;">y</span><span class = "mord mathdefault" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; font - family: KaTeX_Math; font - style: italic; background: transparent;">e</span><span class = "mord mathdefault" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; font - family: KaTeX_Math; font - style: italic; background: transparent;">a</span><span class = "mord mathdefault" style = "box - sizing: border - box; margin: 0px 0.02778em 0px 0px; padding: 0px; border: 0px; outline: 0px; position: static; font - family: KaTeX_Math; font - style: italic; background: transparent;">r</span><span class = "mord mathdefault" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; font - family: KaTeX_Math; font - style: italic; background: transparent;">s</span></span></span></span></span><br style = "box - sizing: border - box; font - family: Karla; font - size: 18px; letter - spacing: - 0.36px; line - height: 25.2px; background - color: #ffffff;" /><span style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; font - size: 18px; font - family: Karla; letter - spacing: - 0.36px; line - height: 25.2px; background: #ffffff;">B's age <span class = "katex" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; font - size: 1em; font - weight: inherit; font - stretch: normal; font - family: KaTeX_Main, 'Times New Roman', serif; line - height: inherit; text - rendering: auto; position: relative; background: transparent;"><span class = "katex - html" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;" aria - hidden = "true"><span class = "base" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: relative; display: inline - block; white - space: nowrap; width: min - content; background: transparent;"><span class = "mrel" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;"> = </span></span><span class = "base" style = "box - sizing: border - box; margin: 0px 0px 3px; padding: 0px; border: 0px; outline: 0px; position: relative; display: inline - block; white - space: nowrap; width: min - content; background: transparent;"><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">1</span><span class = "mord" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; background: transparent;">5</span><span class = "mord mathdefault" style = "box - sizing: border - box; margin: 0px 0.03588em 0px 0px; padding: 0px; border: 0px; outline: 0px; position: static; font - family: KaTeX_Math; font - style: italic; background: transparent;">y</span><span class = "mord mathdefault" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; font - family: KaTeX_Math; font - style: italic; background: transparent;">e</span><span class = "mord mathdefault" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; font - family: KaTeX_Math; font - style: italic; background: transparent;">a</span><span class = "mord mathdefault" style = "box - sizing: border - box; margin: 0px 0.02778em 0px 0px; padding: 0px; border: 0px; outline: 0px; position: static; font - family: KaTeX_Math; font - style: italic; background: transparent;">r</span><span class = "mord mathdefault" style = "box - sizing: border - box; margin: 0px; padding: 0px; border: 0px; outline: 0px; position: static; font - family: KaTeX_Math; font - style: italic; background: transparent;">s</span></span></span></span></span></p>
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