Question

$\Large\underline{Question}$

Find a:b:c -:

(i) a:b=$\sf{7\dfrac{1}{2}:5}$
and
b:c=$\sf{1\dfrac{1}{4}:3}$

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Answer 1

Answer:

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Answer 2

Given :

• a : b = $\sf{7\dfrac{1}{2}:5}$

• b : c = $\sf{1\dfrac{1}{4}:3}$

To find : a : b : c

Solution :

$\bullet \sf \: a : b \: = \: \sf{7\dfrac{1}{2}:5} \\ \\ \sf \: a : \: b \: = \: \dfrac{(7 \times 2) + 1}{2} : \: 5 \\ \\ \sf \: a : b \: = \: \dfrac{15}{2} : 5 \\ \\ \sf \: \dfrac{a}{b} \: = \: \dfrac{ \dfrac{15}{2} }{5} \\ \\ \sf \: \dfrac{a}{b} = \: \dfrac{15}{2 \times 5} \\ \\ \sf \: \dfrac{a}{b} \: = \: \dfrac{3}{2} \\ \\ \sf \: a \: = \frac{3}{2} b$

$\bullet \sf \: b : c \: = 1\dfrac{1}{4} : 3 \\ \\ \sf \: b : c = \: \dfrac{(1 \times 4) + 1}{4} : 3 \\ \\ \sf \: b : c = \: \dfrac{5}{4} : 3 \\ \\ \sf \dfrac{b}{c} = \dfrac{ \frac{ \: 5 \: }{ \: 4 \: } }{ \: 3 \: } \\ \\ \sf \: \dfrac{b}{c} = \: \dfrac{5}{4 \times 3} \\ \\ \sf \: b \: \times \dfrac{12}{5} = c$

therefore

a = 3b/2

c = 12b/5

therefore

$\sf \: a : b : c \: = \dfrac{3b}{2} : \: b : \dfrac{12b}{5}$

take LCM of 2&5 , i.e.10

now we have to make denominator of all three equal to 10

therefore,

• multiply & divide 1st by 5
• multiply and divide 2nd by 10
• multiply and divide 3rd by 2

$\sf \dfrac{15b}{10} : \dfrac{10b}{10} : \: \dfrac{24b}{10} \\ \\ \: \sf \: \dfrac{b}{10} \: get \: canceled \ \\ \\ \sf a : b : c \: = \: 15 : 10 : 24$

ANSWER :

• a : b : c = 15 : 10 : 24