Management Exams (CAT) - Quantitative Aptitude (QA)

Advanced Proportions, Mixtures, Time-Speed & Work question bank (Arithmetic & Commercial Mathematics)

Practice 610 free Management Exams (CAT) - Quantitative Aptitude (QA) Arithmetic & Commercial Mathematics - Advanced Proportions, Mixtures, Time-Speed & Work questions with answers and step-by-step solutions.

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Q1.

Time, Speed & Escalators: A commuter walks up a moving upwards escalator in 30 seconds taking 20 steps in 'Time, Speed & Distance: Escalators, Circular Tracks and Relative Speed'. The same commuter walks up the same escalator moving downwards in 90 seconds taking 60 steps. How many steps are visible when the escalator is stationary?

(A)

30 steps ($N = 20 + 30v_e = 60 - 90v_e \implies 120v_e = 40 \implies v_e = 1/3 \implies N = 30$) (Time, Speed & Distance: Escalators, Circular Tracks and Relative Speed)

(B)

40 steps

(C)

45 steps

(D)

50 steps

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Q2.

Geometry (Apollonius Theorem): In $\triangle ABC$ in 'Time, Speed & Distance: Escalators, Circular Tracks and Relative Speed', $AB = 7\text{ cm}$, $AC = 9\text{ cm}$, and median $AD = 7\text{ cm}$. What is the length of side $BC$?

(A)

$8\sqrt{2}\text{ cm} \approx 11.31\text{ cm}$ ($7^2 + 9^2 = 2(7^2 + BD^2) \implies 130 = 2(49 + BD^2) \implies BD^2 = 16 \implies BD = 4 \implies BC = 8$) or $8\text{ cm}$ (Time, Speed & Distance: Escalators, Circular Tracks and Relative Speed)

(B)

10 cm

(C)

12 cm

(D)

14 cm

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