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Three parallel lines cut by two transversals: intercepts are proportional

This type of question, asked 2 times: CDS 1 2018, CDS 1 2019. All 2 questions below, oldest first.

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  1. Question 1

    CDS 1 2018

    97
    In the figure given below, p, q, r are parallel lines; ll and m are two transversals. Consider the following : 1. AB : AC = DE : DF 2. AB×EF=BC×DEAB \times EF = BC \times DE Which of the above is/are correct ?

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  2. Question 2

    CDS 1 2019

    27
    Three parallel lines xx, yy and zz are cut by two transversals mm and nn. Transversal mm cuts the lines xx, yy, zz at PP, QQ, RR respectively; and Transversal nn cuts the lines xx, yy, zz at LL, MM, NN respectively. If PQ=3PQ = 3 cm, QR=9QR = 9 cm and MN=10.5MN = 10.5 cm, then what is the length of LMLM ?

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