Question

Simplify the ratio 2/3 : 5/6 : 7/9 and divide Rs 1230 in the ratio. ​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO DETERMINE

Simplify the ratio 2/3 : 5/6 : 7/9 and divide Rs 1230 in the ratio.

CALCULATION

The given ratio is

$= \displaystyle \sf{ \frac{2}{3} : \frac{5}{6} : \frac{7}{9} \: }$

$\displaystyle \sf{1st \: term \: of \: the \: ratio \: = \frac{2}{3} }$

$\displaystyle \sf{2nd \: term \: of \: the \: ratio \: = \frac{5}{6} \: }$

$\displaystyle \sf{3rd \: term \: of \: the \: ratio \: = \frac{7}{9} \: }$

Now the LCM of the denominators is = 18

So

$\displaystyle {\frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18} } \:$

$\displaystyle {\frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18} } \:$

$\displaystyle {\frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18} } \:$

So the given ratio can be rewritten as

$= \displaystyle \sf{ \frac{12}{18} : \frac{15}{18} : \frac{14}{18} \: }$

$= \displaystyle \sf{ {12} : {15} : 14 \: }$

Which is the simplified form of the given ratio

Now

$\displaystyle \sf{ 1st \: \: share = \frac{12}{12 + 15 + 14} = \frac{12}{41} \: \: }$

$\displaystyle \sf{ 2nd \: \: share = \frac{15}{12 + 15 + 14} = \frac{15}{41} \: \: }$

$\displaystyle \sf{ 3rd \: \: share = \frac{14}{12 + 15 + 14} = \frac{14}{41} \: \: }$

Now dividing the amount Rs 1230 in the given ratio we get

$\displaystyle \sf{ 1st \: \: amount = 1230 \times \frac{12}{41} = 360 \: \: }$

$\displaystyle \sf{ 2nd \: \: amount = 1230 \times \frac{15}{41} = 450 \: \: }$

$\displaystyle \sf{ 3rd \: \: amount = 1230 \times \frac{14}{41} = 420 \: \: }$

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If a : b=c:d=e: f= 2:1

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