Basic Numeracy - Online Test

Q1. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Answer : Option D
Explaination / Solution:

Speed=60 x5m/sec=50m/sec.
183

Length of the train = (Speed x Time).

 Length of the train =50x 9m = 150 m.
3


Q2. A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Answer : Option B
Explaination / Solution:

Speed of the train relative to man =125m/sec
10

   =25m/sec.
2

   =25x18km/hr
25

   = 45 km/hr.

Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.

 x - 5 = 45          x = 50 km/hr.


Q3. Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:
Answer : Option C
Explaination / Solution:

Let AB be the lighthouse and C and D be the positions of the ships.

Then, AB = 100 m, ACB = 30° and ADB = 45°.

AB= tan 30° =1         AC = AB x √3 = 100√3 m.
AC√3

AB= tan 45° = 1          AD = AB = 100 m.
AD

 CD = (AC + AD)= (100√3 + 100) m
= 100(√3 + 1)
= (100 x 2.73) m
= 273 m.


Q4. The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:
Answer : Option D
Explaination / Solution:

Let AB be the wall and BC be the ladder.

Then, ACB = 60º and AC = 4.6 m.

AC= cos 60º =1
BC2

 BC= 2 x AC
= (2 x 4.6) m
= 9.2 m.


Q5. A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
Answer : Option C
Explaination / Solution:

S.I. for 1 year = Rs. (854 - 815) = Rs. 39.

S.I. for 3 years = Rs.(39 x 3) = Rs. 117.

 Principal = Rs. (815 - 117) = Rs. 698.


Q6. Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?
Answer : Option A
Explaination / Solution:

Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 - x).

Then,x x 14 x 2+(13900 - x) x 11 x 2= 3508
100100

 28x - 22x = 350800 - (13900 x 22)

 6x = 45000

 x = 7500.

So, sum invested in Scheme B = Rs. (13900 - 7500) = Rs. 6400.


Q7. The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:
Answer : Option B
Explaination / Solution:

Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x.

S.P. of x articles = Rs. 20.

Profit = Rs. (20 - x).

20 - xx 100 = 25
x

 2000 - 100x = 25x

125x = 2000

 x = 16.


Q8. In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
Answer : Option B
Explaination / Solution:

Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420.

New C.P. = 125% of Rs. 100 = Rs. 125

New S.P. = Rs. 420.

Profit = Rs. (420 - 125) = Rs. 295.

 Required percentage =295x 100%=1475% = 70% (approximately).
42021


Q9. Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:
Answer : Option C
Explaination / Solution:

Let their marks be (x + 9) and x.

Then, x + 9 =56(x + 9 + x)
100

 25(x + 9) = 14(2x + 9)

 3x = 99

 x = 33

So, their marks are 42 and 33.


Q10. A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:
Answer : Option D
Explaination / Solution:

Suppose originally he had x apples.

Then, (100 - 40)% of x = 420.

60x = 420
100

 x =420 x 100  = 700.
60