Question

A line segment AP is divided into 2 parts by a point O. If the length of the smaller segment AO is 15 cm less than the larger segment OP and the ratio of lengths of AO and OP = 4 : 7, find the length of OP.

• A. 42 cm
• B. 28 cm
• C. 35 cm
• D. 21 cm

Answer 1

The correct option is C

35 cm

AO : OP = 4 : 7 (given)

Let AO be 4x and OP be 7x

AO = OP - 15 (given)

$\Rightarrow 4x=7x-15$

$\Rightarrow 7x-4x=15$

$\Rightarrow 3x=15$

$\Rightarrow x=\frac{15}{3}=5$

Hence, length of OP $=7x=7\times 5=35$ cm.