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Question

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

A
4 : 5
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B
2 : 3
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C
6 : 5
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D
4 : 9
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Solution

The correct option is C 6 : 5
Given AP : PQ = 1 : 2 and PQ : QB = 4 : 5
APPQ=12APPQ+1=12+1AP+PQPQ=32AQPQ=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.

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