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1600 CAT Questions, 300 Video Solutions and 41 Topic Wise Tests

CAT Algebra questions from Linear equations and Quadratic equations that appear in the Quantitative Aptitude section of the CAT Exam consists of concepts from Equations and Algebra. Get as much practice as you can in these two topics because the benefits of being good at framing equations can be enormous and useful in other CAT topics as well. In CAT Exam, one can generally expect to get 1~2 questions from Linear Equations and Quadratic Equations. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.

Algebra

Following questions have two quantities as Quantity I and Quantity II. You have to determine the relationship between them and give answer as,

Q1.

Quantity I: A man can row at a speed of 8.5 kmph in still water and he rows the same distance up and down in a stream which river flows at a rate of 1.5 km/hr. Then his average speed throughout the journey.

Quantity II:  Speed of a cyclist, cycling in a circular ground of radius 14 kilometer if he takes 8 hours to complete onefull round of the ground.

: min

Quantity I:

D= downstream, U= upstream, X= speed in still water

Average Speed = U × D/X

X= 8.5 kmph

D= (8.5+1.5) = 10 kmph , U = (8.5 –1.5) = 7 kmph

Average Speed = 10 × 7/8.5 = 70/8.5= 8.23 kmph.

Quantity II:

Distance(Circumference) = 2 × π × r = 2 × 22/7 × 14= 88 km ; Time = 8 hours
Speed = 88/8 = 11 kmph
Hence Quantity II > Quantity I.

Q2.

A man can row 12 kmph in still water. It takes him twice as long to row up as to row down the river.

Quantity I: Rate of stream.

Quantity II: Speed of a man in still water who can row upstream at 6 kmph and downstream at 2 kmph.

: min

Quantity I:

y= Rate of stream

12+y= 2(12-y)
 y= 4 kmph.

Quantity II:

x = (6+2)/2= 4kmph

Hence, Quantity I = Qunatity II.

Q3.

Quantity I:  Annual Salary of Rohit after tax deduction if he earns Rs 40000 per month and pays a tax of 20% each month.

Quantity II: A and B started a business with Rs 15,000 and Rs 21,000 respectively. After 6 months C joined them with Rs 30,000. B′s share in total profit of Rs 780000 at the end of 2 years.

: min

Quantity I: Salary after deducation = 40000×12×80/100 = Rs 384000.

Quantity II: A:B:C = 15000×24 : 21000×24 : 30000*18=10:14:15
            B=14/39 ×780000= Rs 280,000.

Hence, Quantity I < Qunatity II.

Q4.

Quantity I: x² - 18.75 - 11.25 = 11% of 400 + 287.

Quantity II: y² + 400 ÷ 16 – 18 × 14 = 18 + √121.

: min

Quantity I:

x² - 18.75 - 11.25 = 11% of 400 + 287

=> x² - 18.75 - 11.25 = 11% of 400 + 287

=> x² - 30 = 11% of 400 + 287

=> x² - 30 = 11/100 × 400 + 287

=> x² - 30 = 44 + 287

=> x² = 361

  x= 19

Quantity II:

y²+400÷16-18×14=18+√121

=>y²+25-18×14=18+11

=>y²+25-18×14=29

=>y²+25-252=29

=>y²=29+252-25

=>y²=256

   y=16

Hence, Quantity I > Qunatity II.