Question 56

A race course is 400 metres long. A and B run a race and A wins by 5 metres. B and C run over the same course and B wins by 4 metres. C and D run over it and D wins by 16 metres. If A and D run over it, then who would win and by how much?

Solution

A wins over B by 5 m :
$$\dfrac{\ V_A}{V_B}=\dfrac{\ 400}{395}=\dfrac{\ 80}{79}$$

B wins over C by 4 m :
$$\dfrac{\ V_B}{V_C}=\dfrac{\ 400}{396}=\dfrac{\ 100}{99}$$

D wins over C by 16 m :
$$\dfrac{\ V_D}{V_C}=\dfrac{\ 400}{384}=\dfrac{\ 25}{24}$$

$$\rightarrow$$ Hence, $$\left(\dfrac{\ V_A}{V_B}\right)\ \left(\dfrac{\ V_B}{V_C}\right)\ \left(\dfrac{\ V_C}{V_D}\right)=\ \dfrac{\ 80}{79}\times\dfrac{\ 100}{99}\times\dfrac{\ 24}{25}$$

$$=\ \dfrac{\ V_A}{V_D}=\ \dfrac{\ 80\times32}{79\times33}$$

$$=\dfrac{V_A}{V_D}=\ \dfrac{2560\ }{2607}=\ \dfrac{\ 400-x}{400}$$

Therefore, $$x=7.21\ m$$ .

Therefore, D wins over A by 7.21 metres.

Video Solution

video

View More Questions From Time, Speed and Distance

Create a FREE account and get:

All Quant Formulas and Shortcuts PDF
100+ previous papers with solutions PDF
Top 5000+ MBA exam Solved Questions for Free

maruti sir image

MAT Quant Questions | MAT Quantitative Ability

MAT Profit And Loss Questions MAT Profit and Loss Questions MAT Mensuration Questions MAT Logarithms Questions MAT Averages Mixtures Alligations Questions MAT Geometry Questions MAT Algebra Questions MAT Coordinate Geometry Questions MAT Time Speed Distance Questions MAT Quadratic Equations Questions MAT Arithmetic Questions MAT Functions, Graphs and Statistics Questions MAT Percentages Questions MAT Progressions and Series Questions MAT Number Systems Questions MAT Venn Diagrams Questions MAT Time And Work Questions MAT Averages, Ratio and Proportion Questions MAT Averages Questions MAT Logarithms, Surds and Indices Questions MAT Number Series Questions MAT Time, Speed and Distance Questions MAT Linear Equations Questions MAT Data Sufficiency Questions MAT Remainders Questions MAT Inequalities Questions MAT Probability, Combinatorics Questions MAT Simple Interest Compound Interest Questions

MAT DILR Questions | LRDI Questions For MAT

MAT Arrangement Questions MAT Quant Based LR Questions MAT Coins and Weights Questions MAT Table based DI Sets Questions MAT Data change over a period Questions MAT Data Interpretation Questions MAT Data Interpretation Basics Questions MAT Charts Questions MAT Games and Tournamnents Questions MAT DI with connected data sets Questions MAT Truth Lie Concept Questions MAT Special Charts Questions MAT Maxima-Minima Questions MAT Quant Based DI Questions MAT 2D & 3D LR Questions MAT Miscellaneous LR Questions MAT Routes And Networks Questions MAT DI Miscellaneous Questions MAT Puzzles Questions MAT Venn Diagrams Questions MAT Selection With Condition Questions MAT Scheduling Questions

MAT Verbal Ability Questions | VARC Questions For MAT

MAT Para Jumbles Questions MAT Miscellaneous Questions MAT Critical Reasoning Questions MAT Reading Comprehension Questions MAT Vocabulary Questions MAT Odd One Out Questions MAT Grammar and Sentence Correction Questions MAT Verbal Ability Questions MAT Para Summary Questions