Question

(c) If a: b = 12:5 and b:c =15:8 then find the reciprocal ratio of a :c.​

Answer 1

$\textsf{\large{\underline{Solution}:}}$

Given:

$\rm: \longmapsto a :b =12 : 5$

$\rm: \longmapsto b:c =15 : 8$

Therefore:

$\rm: \longmapsto \dfrac{a}{b} = \dfrac{12}{5} - (i)$

$\rm: \longmapsto \dfrac{b}{c} = \dfrac{15}{8} - (ii)$

Multiplying (i) and (ii), we get:

$\rm: \longmapsto \dfrac{a}{b} \times \dfrac{b}{c} = \dfrac{12}{5} \times \dfrac{15}{8}$

$\rm: \longmapsto \dfrac{a}{b} \times \dfrac{b}{c} = \dfrac{9}{2}$

$\rm: \longmapsto \dfrac{a}{c} = \dfrac{9}{2}$

$\rm: \longmapsto a : c =9: 2$

★ Therefore, reciprocal ratio of a : c is c : a or 2 : 9.

$\textsf{\large{\underline{More To Know}:}}$

If a : b and c : d are two ratios such that a : b : : c : d. Then the following results hold true.

1. Invertendo.

$\rm:\longmapsto b : a : : d : c$

2. Alternendo.

$\rm:\longmapsto a : c : : b : d$

3. Componendo.

$\rm:\longmapsto (a + b) : b: : (c + d) : d$

4. Dividendo.

$\rm:\longmapsto (a - b) : b: : (c - d) : d$

5. Componendo and dividendo.

$\rm:\longmapsto (a + b) : (a - b): : (c + d) :(c - d)$

6. Convertendo.

$\rm:\longmapsto a : (a - b): :c:(c - d)$

Answer 2

Answer:

HELLO BUDDY,

Step-by-step explanation:

$[tex]\textsf{\large{\underline{Solution}:}}$

Given:

$\rm: \longmapsto a :b =12 : 5$

$\rm: \longmapsto b:c =15 : 8$

Therefore:

$\rm: \longmapsto \dfrac{a}{b} = \dfrac{12}{5} - (i)$

$\rm: \longmapsto \dfrac{b}{c} = \dfrac{15}{8} - (ii)$

Multiplying (i) and (ii), we get:

$\rm: \longmapsto \dfrac{a}{b} \times \dfrac{b}{c} = \dfrac{12}{5} \times \dfrac{15}{8}$

$\rm: \longmapsto \dfrac{a}{b} \times \dfrac{b}{c} = \dfrac{9}{2}$

$\rm: \longmapsto \dfrac{a}{c} = \dfrac{9}{2}$

$\rm: \longmapsto a : c =9: 2$

★ Therefore, reciprocal ratio of a : c is c : a or 2 : 9.

$\textsf{\large{\underline{More To Know}:}}$

If a : b and c : d are two ratios such that a : b : : c : d. Then the following results hold true.

1. Invertendo.

$\rm:\longmapsto b : a : : d : c$

2. Alternendo.

$\rm:\longmapsto a : c : : b : d$

3. Componendo.

$\rm:\longmapsto (a + b) : b: : (c + d) : d$

4. Dividendo.

$\rm:\longmapsto (a - b) : b: : (c - d) : d$

5. Componendo and dividendo.

$\rm:\longmapsto (a + b) : (a - b): : (c + d) :(c - d)$

6. Convertendo.

$\rm:\longmapsto a : (a - b): :c:(c - d)$[/tex]