# Linear Equations ( 11 to 15 )

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Linear Equations ( 11 to 15 ):

# APTITUDE QUESTIONS (LINEAR EQUATIONS):

11. The distance between two stations is 340 km. two trains start simultaneously from these stations on parallel tracks to cross each other. The speed of one of them is greater than that of other by 5 km/h. If the distance between the two trains after 2 hours of their start is 30 km, then the speed of each train are

A)    75 km/h, 80 km/h

B)    60 km/h, 65 km/h

C)    80 km/h, 85 km/h

D)    55km/h, 60km/h

E)    None of these

Explanation:
Let speed of first train = x km/h and speed of second train = x + 5km/h
Distance travelled in 2 h by first train = 2x km/h
Distance travelled in 2 h by second train = (x + 5) * 2 km
As 2x + (2x + 10) + 30 = 340
=> 4x = 340
=> x = 75
Speed of first train = 75 km/h and speed of second train = 80 km/h.

12. A streamer goes downstream and covers the distance between two ports in 4 hours while it covers the same distance upstream in 5 hours. If the speed of the stream is 2 km/hr, then the speed of the stream in still water is:

A)    20km/h

B)    19 km/h

C)    18 km/h

D)    19.5 km/h

E)    None of these

Explanation:
Let the speed of the streamer in still water = x km/h
Speed of streamer downstream = (x + 2) km/h
Speed of streamer upstream = (x – 2) km/h
Distance travelled by streamer in downstream in 4 hours = 4(x + 2) km
So, 4(x + 2) = 5(x – 2) km
=> x = 18km/h is the speed in still water

13. The sum of two numbers is 2490 and if 6.5% of one number is equal to 8.5% of the other, then numbers are

A)    1414, 1076

B)    1411, 1079

C)    1412, 1078

D)    1413, 1077

E)    None of these

Explanation:
Let the numbers be x and 2490 – x
6.5 % of one = (6.5/100)* x = (13x/200)
8.5 % of other number = (8.5/100)(2490 – x) = (17/200)(2490 – x)
By condition, (13x/200) = ((17/200)(2490-x))
=> 13x = 17(2490 – x)
=> 13x + 17x = 42330
=> x = (42330/30) = 1411
Second number = 2490 – 1411 = 1079

14. Three prizes are to be distributed in a quiz contest. The value of the second prize is five-sixth of the value of the first price and the value of the third prize is four-fifth of that of the second prize. If the total value of the three prizes is Rs.150, then the value of each price is respectively

A)    Rs. 60, Rs.40, Rs.50

B)    Rs.55, Rs.45, Rs.50

C)    Rs.50, Rs.40, Rs.60

D)    Rs.60, Rs.50, Rs.40

E)    None of these

Explanation:
Let the value of first prize be Rs.x
Value of second prize = Rs.(5/6) x
Value of third prize = (4/5) [(5/6)x] = Rs (2/3) x
as (2/3)x + (5/6)x + x = 150
=> 15x/6 = 150 => x = 60
=> Hence, value of first prize = Rs.60
=> Value of second prize= (5/6) * 60 = Rs.50
=> Value of third prize= (2/3) * 60 = Rs.40

15. One of the angle of a triangle is equal to the sum of the other two angles. If the ratio of the other two angles is 4:5, then the angles of triangle are

A)    90°, 40°, 50°

B)    15°, 60°, 105°

C)    30°, 60°, 90°

D)    30°, 40°, 110°

E)    None of these

Explanation:
Let the two angles be 4x and 5x
Then third angle = 4x + 5x = 9x
So, 4x + 5x + 9x = 180

=> 18x = 180
=> x = 10
=> so, angles are 4x = 40°
=> 5x = 5* 10 = 50°
=> 9x = 9 * 10 = 90°