Question

If p: q = 3: 4 and q: r = 6 : 7, then find i) p : r ii) p : q : r

Answer 1

Answer:

Answer:3640

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Answer 2

If $p:q=3:4$  and  $q:r=6:7$ , then 1) $p:r =9:14$  and 2) $p:q:r=9:12:14$ .

Step-by-step explanation:

We are given with two ratios,

$p:q=3:4$  

$q:r=6:7$  

and we have to find the ratios 1) $p:r$   and 2)  $p:q:r$ .

• 1) Ratio of  $p:r$

for calculating ratio of $p:r$  we have to find the value of p in terms of r.

by using first ratio we can write,

$\frac{p}{q} =\frac{3}{4}$

$p=\frac{3}{4}* q$        --(1)

we will calculate q from second ratio

 $q:r=6:7$

$\frac{q}{r} =\frac{6}{7}$

$q=\frac{6}{7} *r$

put this q  in equation (1)

$p=\frac{3}{4} *\frac{6}{7} *r$

$\frac{p}{r} =\frac{3}{4} *\frac{6}{7}$

   $=\frac{9}{14}$

so the ratio of $q:r=6:7$.

• 2) Ratio of  $p:q:r$

we write p and q in terms of r,

$p=\frac{9}{14} *r$       and      $q=\frac{6}{7} *r$

so the ratio is,

$p:q:r=\frac{9}{14}r :\frac{6}{7}r :r$

            $=\frac{9}{14} :\frac{6}{7} :1$

taking L.C.M of 14 and 7,  

L.C.M of 14 and 7 is 14.

             $=\frac{(9):(6*2):(1*14)}{14}$

             $=9:12:14$

so the ratio as  $p:q:r=9:12:14$.

We get the answer as $p:r =9:14$  and  $p:q:r=9:12:14$ .