Ratio, Proportion, Indices and Logarithm | CA Foundation | Ex 1 A (16)

All CA Foundation Exercises solved!
Course : 𝐂𝐀 𝐅𝐨𝐮𝐧𝐝𝐚𝐭𝐢𝐨𝐧 May, 2022 examination onwards | Topic : 𝐑𝐚𝐭𝐢𝐨, 𝐏𝐫𝐨𝐩𝐨𝐫𝐭𝐢𝐨𝐧, 𝐈𝐧𝐝𝐢𝐜𝐞𝐬 𝐚𝐧𝐝 𝐋𝐨𝐠𝐚𝐫𝐢𝐭𝐡𝐦
Exercise - 𝟏 (𝐀)
𝐐𝐮𝐞𝐬𝐭𝐢𝐨𝐧 𝐍𝐮𝐦𝐛𝐞𝐫 : 𝟏𝟔 - Anand earns ₹ 80 in 7 hours and Pramod ₹ 90 in 12 hours. The ratio of their earnings is …?
𝐎𝐩𝐭𝐢𝐨𝐧 (𝐀) : (32 : 21)
𝐎𝐩𝐭𝐢𝐨𝐧 (𝐁) : (23 : 12)
𝐎𝐩𝐭𝐢𝐨𝐧 (𝐂) : (8 : 9)
𝐎𝐩𝐭𝐢𝐨𝐧 (𝐃) : None of these

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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 16 from Exercise 1A. The question is... Anand earns rupees 80 in seven hours and Pramod earns rupees 90 in 12 hours. The ratio of their earnings is....? Now; if you see; the amounts are different and the timings are also different. So; in order to find the ratio... what we do is... we first calculate the earnings of both of these people; that is Anand and Pramod in terms of earnings per hour. So, let us calculate that... so we could say Anand's earnings per hour would be... now 80 rupees in seven hours; so we have 80 / 7 in 1 hour; right; so in seven hours he earns 80 rupees; so in one hour he would earn 80 by 7. So this is the earnings per hour for Anand. Similarly we calculate Pramod's earnings. Pramod's earnings per hour... Now he earns 90 rupees in 12 hours.. so he would earn 90 by 12 rupees per hour and now we could make the comparison. So therefore we could say; the ratio of their earnings; the ratio of their earnings is 80 divided by 7 is to 90 by 12. Now let us simplify this! So here we have 80 by 7 into this! would become 12 by 90. Simplifying further.. we can cancel the zeros over here.. 3 x 4 is 12; 3 x 3 is 9. So 8 x 4; that's 32 and 7 x 3 that's 21; So the required ratio is 32 is 221. Let us check the option. Yes! the correct answer is option A : 32 is to 21.

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𝐋𝐞𝐚𝐫𝐧𝐢𝐧𝐠 𝐎𝐛𝐣𝐞𝐜𝐭𝐢𝐯𝐞 - How to solve word problem relating to ratios and earnings?
𝐂𝐨𝐧𝐜𝐞𝐩𝐭𝐬
✔️A ratio is a comparison of the sizes of two or more quantities of the same kind by division.
✔️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.