# Linear Equations ( 16 to 20 )

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Linear Equations ( 16 to 20 ):

# APTITUDE QUESTIONS (LINEAR EQUATIONS):

16. Two planes start from a city and fly in opposite directions, one averaging a speed of 40 km/h greater than the others. If they are 3400 km apart after 5 hours, the average speeds respectively are

A) 330, 370 km/h

B) 320, 360 km/h

C) 250, 290 km/h

D) 300, 340 km/h

E) None of these

Explanation:
Let average speed of one plane be x km/h
Then average speed of other plane be (x + 40) km/h
Distance travelled by first plane in 5 hours = 5x km
Distance travelled by second plane in 5 hours = 5(x + 40) km
So, 5x + 5(x + 40) = 3400
10x + 200 = 3400
10x = 3200
x = 3200/10 = 320km/hr
so, average speed of second plane = 320 + 40 = 360 Km/h

17. If a scooterist drives at the rate of 24km/h, he reaches his destination 5 minutes too late; if he drives at the rate of 30km/h, he reaches his destination 4 minutes too soon. Then his destination is at a distance of

A)    20 km

B)    30 km

C)    25 km

D)    18 km

E)    None of these

Explanation:
Let the required distance be x km
With the two speeds, the difference of time taken = 9min
∴ (x/24) – (x/30) = (9/60)
=>(x/120) = (9/60)

=>(x/2) = 9

=>x=18km

18. Sum of two numbers is 21 and their difference is 11, then the greatest number is

A)    5

B)    16

C)    9

D)    10

E)    None of these

Explanation:
Let numbers be x and y, then
x + y = 21      …(i)
x – y = 11      …(ii)
on adding eqs. (i) and (ii)
2x = 32

=>x = (32/2) = 16

19. Which of the following equations have x = 2 and y = 1 as a solution?

i.)2x + 5y = 9     ii.) 5x + 3y = 14     iii.) 2x + 3y = 7     iv.) 2x – 3y = 1

A)    i and iv

B)    ii and iii

C)    only i

D)    i, iii and iv

E)    None of these

Explanation:
Put x = 2 and y =1 in each equation
2x + 5y = 9

=>2(2) + 5(1) = 9

=>9 = 9 it is true
2x + 3y = 7

=>2(2) + 3(1) = 7

=>7 = 7 it is true
2x – 3y = 1

=>2(2) – 3(1) = 1

=>1 = 1 it is true
So, x =2 and y = 1 is solution of above equations but for 5x + 3y = 14, 5(2) + 3(1) = 14

=>13≠14

=>x = 2 and y =1 is not a solution

20. The line 3x – 5y = -10 cuts y axis at

A) (0,2)

B) (0,1)

C) (0,3)

D) (0,4)

E) None of these

Explanation:
Here, 3x – 5y = 10
At y-axis x = 0, put in equation
0 – 5y = -10
y = (10/5) = 2

∴ Point on y-axis is (0,2)