If AP : PQ = 1 : 2 and PQ : QB = 4 : 5, then Q divides line segment AB in the ratio .

4 : 5

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2 : 3

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6 : 5

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4 : 9

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Solution

The correct option is C 6 : 5
Given AP : PQ = 1 : 2 and PQ : QB = 4 : 5
$\frac{A P}{P Q} = \frac{1}{2} \Rightarrow \frac{A P}{P Q} + 1 = \frac{1}{2} + 1 \Rightarrow \frac{A P + P Q}{P Q} = \frac{3}{2} \Rightarrow \frac{A Q}{P Q} = \frac{3}{2} - - - (1) \frac{Q B}{P Q} = \frac{5}{4} - - - (2)$
Dividing equation (1) by (2),
$\Rightarrow \frac{A Q}{Q B} = \frac{6}{5}$
Hence, Q divides the line segment AB in the ratio of 6 : 5.

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Q. If AP : PQ = 1 : 2 and PQ : QB = 4 : 5, then Q divides line segment AB in the ratio .

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Q. How do we identify two points P and Q on a line segment AB such that AP : PQ = 1 : 2 and PQ : QB = 4 : 5?

Points P and Q are in the line segment AB and on the same side of its midpoint. P divides AB in the ratio 2:3 and Q divides AB in the ratio 3:4. If $P Q = 2 c m,$ then find the length of the line segment AB.

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If AP : PQ = 1 : 2 and PQ : QB = 4 : 5, then Q divides line segment AB in the ratio .

The correct option is C 6 : 5Given AP : PQ = 1 : 2 and PQ : QB = 4 : 5 APPQ=12⇒APPQ+1=12+1⇒AP+PQPQ=32⇒AQPQ=32 −−−(1)QBPQ=54 −−−(2) Dividing equation (1) by (2), ⇒AQQB=65 Hence, Q divides the line segment AB in the ratio of 6 : 5.