Ratio, Proportion, Indices and Logarithm | CA Foundation | Ex 1 A (3)

All CA Foundation Exercises solved!

Course : 𝐂𝐀 𝐅𝐨𝐮𝐧𝐝𝐚𝐭𝐢𝐨𝐧 May, 2022 examination onwards | Topic : 𝐑𝐚𝐭𝐢𝐨, 𝐏𝐫𝐨𝐩𝐨𝐫𝐭𝐢𝐨𝐧, 𝐈𝐧𝐝𝐢𝐜𝐞𝐬 𝐚𝐧𝐝 𝐋𝐨𝐠𝐚𝐫𝐢𝐭𝐡𝐦
Exercise - 𝟏 (𝐀)
𝐐𝐮𝐞𝐬𝐭𝐢𝐨𝐧 𝐍𝐮𝐦𝐛𝐞𝐫 : 𝟑 - The ratio of the quantities is 5 : 7. If the consequent of its inverse ratio is 5, the antecedent is …?
𝐎𝐩𝐭𝐢𝐨𝐧 (𝐀) : 5
𝐎𝐩𝐭𝐢𝐨𝐧 (𝐁) : √5
𝐎𝐩𝐭𝐢𝐨𝐧 (𝐂) : 7
𝐎𝐩𝐭𝐢𝐨𝐧 (𝐃) : None of these

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𝐒𝐡𝐨𝐫𝐭 𝐍𝐨𝐭𝐞𝐬:
𝐂𝐨𝐧𝐜𝐞𝐩𝐭𝐬 𝐨𝐟 𝐑𝐚𝐭𝐢𝐨𝐬
✔️ A ratio is a comparison of the sizes of two or more quantities of the same kind by division.
✔️If p and q are two quantities of the same kind, then the fraction p/q is called the ratio of p to q.
✔️The quantities p and q are called terms of the ratio.
✔️The first term p is called antecedent.
✔️The second term q is called consequent.
✔️Both the terms of a ratio can be multiplied or divided by the same non-zero number.
✔️Usually a ratio is expressed in lowest terms.
✔️The order of the terms in a ratio is important.
✔️Ratio exists only between quantities of the same kind. Quantities to be compared must be in same units.
✔️To compare two ratios, convert them into equivalent like fractions.

𝐏𝐫𝐨𝐩𝐞𝐫𝐭𝐢𝐞𝐬 𝐨𝐟 𝐑𝐚𝐭𝐢𝐨𝐬
✔️A ratio a : b is said to be of greater inequality if a greater than b and of less inequality if a less than b.
✔️The ratio compounded of the two ratios a : b and c : d is ac : bd.
✔️The inverse ratio of a : b is b : a
✔️The duplicate ratio of a : b is a² : b²
✔️The triplicate ratio of a : b is a³ : b³
✔️The sub-duplicate ratio of a : b is √a : √b
✔️The sub-triplicate ratio of a : b is ³√a : ³√b
✔️If the ratio of two similar quantities can be expressed as a ratio of two integers, the quantities are said to be commensurable, otherwise, they are said to be incommensurable.
✔️Continued ratio is the relation or comparison between the magnitude of three or more quantities of the same kind.

𝐓𝐫𝐚𝐧𝐬𝐜𝐫𝐢𝐩𝐭 / 𝐒𝐮𝐛𝐭𝐢𝐭𝐥𝐞𝐬
𝑾𝒆 𝒏𝒐𝒘 𝒅𝒊𝒔𝒄𝒖𝒔𝒔 𝒒𝒖𝒆𝒔𝒕𝒊𝒐𝒏 𝒏𝒖𝒎𝒃𝒆𝒓 3 𝒇𝒓𝒐𝒎 𝒆𝒙𝒆𝒓𝒄𝒊𝒔𝒆 1𝑨. 𝑻𝒉𝒆 𝒒𝒖𝒆𝒔𝒕𝒊𝒐𝒏 𝒊𝒔.... 𝑻𝒉𝒆 𝒓𝒂𝒕𝒊𝒐 𝒐𝒇 𝒒𝒖𝒂𝒏𝒕𝒊𝒕𝒊𝒆𝒔 𝒊𝒔 5 𝒊𝒔 𝒕𝒐 7. 𝑰𝒇 𝒕𝒉𝒆 𝒄𝒐𝒏𝒔𝒆𝒒𝒖𝒆𝒏𝒕 𝒐𝒇 𝒊𝒕𝒔 𝒊𝒏𝒗𝒆𝒓𝒔𝒆 𝒓𝒂𝒕𝒊𝒐 𝒊𝒔 5, 𝒕𝒉𝒆 𝒂𝒏𝒕𝒆𝒄𝒆𝒅𝒆𝒏𝒕 𝒊𝒔...? 𝑺𝒐 𝒘𝒆 𝒉𝒂𝒗𝒆 𝒕𝒉𝒆 𝒓𝒂𝒕𝒊𝒐 5 𝒊𝒔 𝒕𝒐 7 𝒂𝒏𝒅 𝒕𝒉𝒆 𝒒𝒖𝒆𝒔𝒕𝒊𝒐𝒏 𝒉𝒂𝒔 𝒈𝒊𝒗𝒆𝒏 𝒕𝒉𝒆 𝒄𝒐𝒏𝒔𝒆𝒒𝒖𝒆𝒏𝒕 𝒐𝒇 𝒕𝒉𝒆 𝒊𝒏𝒗𝒆𝒓𝒔𝒆 𝒓𝒂𝒕𝒊𝒐...𝒔𝒐 𝒘𝒉𝒂𝒕 𝒘𝒆 𝒅𝒐 𝒊𝒔 𝒘𝒆 𝒕𝒂𝒌𝒆 𝒕𝒉𝒆 𝒊𝒏𝒗𝒆𝒓𝒔𝒆 𝒓𝒂𝒕𝒊𝒐 𝒐𝒇 5 𝒊𝒔 𝒕𝒐 7... 𝒔𝒐 𝒕𝒉𝒆 𝒊𝒏𝒗𝒆𝒓𝒔𝒆 𝒓𝒂𝒕𝒊𝒐 𝒐𝒇 5 𝒊𝒔 𝒕𝒐 7 𝒊𝒔 7 𝒊𝒔 𝒕𝒐 5. 𝑵𝒐𝒘 𝒊𝒇 𝒕𝒉𝒆 𝒄𝒐𝒏𝒔𝒆𝒒𝒖𝒆𝒏𝒕 𝒊𝒔 5; 𝒚𝒆𝒔! 𝒘𝒆 𝒄𝒂𝒏 𝒔𝒆𝒆 𝒕𝒉𝒂𝒕 𝒕𝒉𝒆 𝒄𝒐𝒏𝒔𝒆𝒒𝒖𝒆𝒏𝒕 𝒉𝒆𝒓𝒆 𝒊𝒔 5; 𝒔𝒐 𝒕𝒉𝒆 𝒄𝒐𝒏𝒔𝒆𝒒𝒖𝒆𝒏𝒕 𝒊𝒔 5; 𝒕𝒉𝒆𝒏 𝒕𝒉𝒆 𝒂𝒏𝒕𝒆𝒄𝒆𝒅𝒆𝒏𝒕 𝒊𝒔...? 𝑺𝒐 𝒉𝒆𝒓𝒆 𝒕𝒉𝒆 𝒂𝒏𝒕𝒆𝒄𝒆𝒅𝒆𝒏𝒕 𝒊𝒔 7. 𝑺𝒐 𝒘𝒆 𝒉𝒂𝒗𝒆 𝒕𝒉𝒆 𝒂𝒏𝒕𝒆𝒄𝒆𝒅𝒆𝒏𝒕 𝒂𝒔 7. 𝑺𝒐 𝒕𝒉𝒆 𝒓𝒆𝒒𝒖𝒊𝒓𝒆𝒅 𝒂𝒏𝒔𝒘𝒆𝒓 𝒊𝒔 𝑶𝒑𝒕𝒊𝒐𝒏 𝑪 : 7

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𝐋𝐞𝐚𝐫𝐧𝐢𝐧𝐠 𝐎𝐛𝐣𝐞𝐜𝐭𝐢𝐯𝐞 - What is consequent in a ratio? How to find inverse in a ratio?
𝐂𝐨𝐧𝐜𝐞𝐩𝐭𝐬
✔️A ratio is a comparison of the sizes of two or more quantities of the same kind by division.
✔️If p and q are two quantities of the same kind, then the fraction p/q is called the ratio of p to q.
✔️The quantities p and q are called terms of the ratio.
✔️The first term p is called antecedent.
✔️The second term q is called consequent.
𝐏𝐫𝐨𝐩𝐞𝐫𝐭𝐢𝐞𝐬 𝐨𝐟 𝐑𝐚𝐭𝐢𝐨𝐬
✔️The inverse ratio of a : b is b : a