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

All CA Foundation Exercises solved!
Course : 𝐂𝐀 𝐅𝐨𝐮𝐧𝐝𝐚𝐭𝐢𝐨𝐧 May, 2022 examination onwards | Topic : 𝐑𝐚𝐭𝐢𝐨, 𝐏𝐫𝐨𝐩𝐨𝐫𝐭𝐢𝐨𝐧, 𝐈𝐧𝐝𝐢𝐜𝐞𝐬 𝐚𝐧𝐝 𝐋𝐨𝐠𝐚𝐫𝐢𝐭𝐡𝐦
Exercise - 𝟏 (𝐀)
𝐐𝐮𝐞𝐬𝐭𝐢𝐨𝐧 𝐍𝐮𝐦𝐛𝐞𝐫 : 𝟏 - The inverse ratio of 11 : 15 is
𝐎𝐩𝐭𝐢𝐨𝐧 (𝐀) : 15 : 11
𝐎𝐩𝐭𝐢𝐨𝐧 (𝐁) : √11 : √15
𝐎𝐩𝐭𝐢𝐨𝐧 (𝐂) : 121 : 125
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 𝒕𝒉𝒆 𝒇𝒊𝒓𝒔𝒕 𝒒𝒖𝒆𝒔𝒕𝒊𝒐𝒏 𝒇𝒓𝒐𝒎 𝑬𝒙𝒆𝒓𝒄𝒊𝒔𝒆 1𝑨. 𝑻𝒉𝒆 𝒒𝒖𝒆𝒔𝒕𝒊𝒐𝒏 𝒊𝒔 𝒕𝒉𝒆 𝒊𝒏𝒗𝒆𝒓𝒔𝒆 𝒓𝒂𝒕𝒊𝒐 𝒐𝒇 11 𝒊𝒔 𝒕𝒐 15 𝒊𝒔 ? 𝑺𝒐 𝒕𝒉𝒆 𝒈𝒊𝒗𝒆𝒏 𝒓𝒂𝒕𝒊𝒐 𝒊𝒔 11 𝒊𝒔 𝒕𝒐 15 𝒂𝒏𝒅 𝒘𝒆 𝒉𝒂𝒗𝒆 𝒕𝒐 𝒐𝒃𝒕𝒂𝒊𝒏 𝒕𝒉𝒆 𝒊𝒏𝒗𝒆𝒓𝒔𝒆 𝒓𝒂𝒕𝒊𝒐. 𝑵𝒐𝒘 𝒘𝒆 𝒌𝒏𝒐𝒘 𝒕𝒉𝒂𝒕 𝒊𝒇 𝒂 𝒊𝒔 𝒕𝒐 𝒃 𝒊𝒔 𝒕𝒉𝒆 𝒈𝒊𝒗𝒆𝒏 𝒓𝒂𝒕𝒊𝒐 𝒕𝒉𝒆𝒏 𝒊𝒕𝒔 𝒊𝒏𝒗𝒆𝒓𝒔𝒆 𝒓𝒂𝒕𝒊𝒐 𝒊𝒔 𝒈𝒊𝒗𝒆𝒏 𝒃𝒚 𝒃 𝒊𝒔 𝒕𝒐 𝒂. 𝑺𝒐, 𝒕𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆 11 𝒊𝒔 𝒕𝒐 15 𝒘𝒊𝒍𝒍 𝒉𝒂𝒗𝒆 𝒕𝒉𝒆 𝒊𝒏𝒗𝒆𝒓𝒔𝒆 𝒓𝒂𝒕𝒊𝒐 𝒂𝒔 15 𝒊𝒔 𝒕𝒐 11. 𝑺𝒐 𝒕𝒉𝒆 𝒄𝒐𝒓𝒓𝒆𝒄𝒕 𝒂𝒏𝒔𝒘𝒆𝒓 𝒕𝒐 𝒕𝒉𝒊𝒔 𝒒𝒖𝒆𝒔𝒕𝒊𝒐𝒏 𝒊𝒔 𝑶𝒑𝒕𝒊𝒐𝒏 𝑨.

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𝐋𝐞𝐚𝐫𝐧𝐢𝐧𝐠 𝐎𝐛𝐣𝐞𝐜𝐭𝐢𝐯𝐞 - How to find Inverse 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