Ratios & Proportion
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Q.

Points $A$ and $B$ are both in the line segment $PQ$ and on the same side of its midpoint. $A$ divides $PQ$ in the ratio $2:3$, and $B$ divides $PQ$ in the ratio $3:4$. If $AB=2$, then the length of $PQ$ is:

 A.

70

 B.

75

 C.

80

 D.

85

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Solution:
Option(A) is correct

Let $PA=2x$ and $AB=3x$

and $PB=3y$ and $BQ=4y$

$PB:BQ=3:4$

$PA:QA=2:3$

$PQ=5x=7y$

$x=7/5$.....(i)

From equation (i) and (ii),

Now, $AB=PQ−PA−BQ=7y−4y−2x$

$⇒ 3y−2x=2$ -------------- (ii)

$y=10$ and Hence, $PQ$ = 70.


(2) Comment(s)


Bhargavi Bhat
 ()

It should be QA=3x instead of AB=3x



Saikiran
 ()

One more easier way. (Eliminating from the options)

Take 2:3 = 5 parts, now 70/5=14 (which means 28:42) is one ratio.

Take 3:4 = 7 parts, now 70/7=10 (which means 30:40) is other ratio.

Diff between 30-28 = 2 (dist AB is 2). We get it