Question

If a/b=c/d=e/f, then the value of (anp+cnq+enr)/(bnp+dnq+fnr):​

Answer 1

SOLUTION

GIVEN

$\displaystyle \sf{ \frac{a}{b} = \frac{c}{d} = \frac{e}{f} }$

TO DETERMINE

$\displaystyle \sf{ \frac{anp + cnq + enr}{bnp + dnq + fnr} }$

EVALUATION

Here it is given that

$\displaystyle \sf{ \frac{a}{b} = \frac{c}{d} = \frac{e}{f} }$

Let

$\displaystyle \sf{ \frac{a}{b} = \frac{c}{d} = \frac{e}{f} = k }$

Then

a = bk , c = dk , e = fk

Thus

$\displaystyle \sf{ \frac{anp + cnq + enr}{bnp + dnq + fnr} }$

$\displaystyle \sf{ = \frac{bknp + dknq + fknr}{bnp + dnq + fnr} }$

$\displaystyle \sf{ = \frac{k(bnp + dnq + fnr)}{(bnp + dnq + fnr)} }$

$= \sf{k}$

Therefore

$\displaystyle \sf{ \frac{anp + cnq + enr}{bnp + dnq + fnr} =\frac{a}{b} = \frac{c}{d} = \frac{e}{f} }$

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