An algebra problem by Rakesh Lal
Algebra
Level
1
Points P&Q are both in the line segment AB and on the same side of its mid point. P divides AB in the ratio 2:3 and Q divides AB in the ratio 3:4. If PQ=2, then find the length of the line segment AB.
70
210
166
140
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1 solution
P&Q are closer to A since ratios are 2:3 and 3:4. AP/AB=2/5. AQ/AB=3/7. PQ=(3/7 - 2/5) AB = 1/35 AB. Since PQ=2, therefore, AB = 2 * 35 = 70.