## Speed Distance & Time, Compound Interest

Aptitude Solved Problem

Questions :

1. A 600m long train is running at 90 Kmph. how much time it will take to cross an electric pole?

2. One card is randomly drawn from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen or King)

3. At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?

4. A bag contains 50 P, 25 P and 10 P coins in the ratio 5 : 9 : 4, amounting to Rs. 206. Find the number of coins of each type respectively.

1. 20 seconds.

2. ( 3 / 13 ).

3. 6 %.

4. 200, 360, 160.

1. Explanation:

Distance = Speed * Time
600 = 90 Kmph * Time
600 = [ 90 * ( 5 / 18 ) ] * Time
600 = 30 * Time
= 600 / 30
= 20 Sec

∴ It will take 20 seconds to cross an electric pole.

2. Explanation:

Total number of cards, n ( S ) = 52
Total number of face cards, n ( E ) = 12
P ( E ) = n ( E ) / n ( S )
= ( 12 / 52 )
= ( 3 / 13 )

∴ The probability is ( 3 / 13 )

3. Explanation:

Let the rate be R% per annum.
Then, 1200 * [ ( 1 + R ) / 100 ]2 = 1348.32
[ 1 + ( R / 100 ) ]2 = 134832 / 120000
[ 1 + ( R / 100 ) ]2 = ( 11236 / 10000 )
[ 1 + ( R / 100 ) ]2 = ( 106 / 100 )2
1 + ( R / 100 ) = 106 / 100
( R / 100 ) = ( 106 / 100 ) – 1
( R / 100 ) = ( 106 – 100 ) / 100
R = ( 6 * 100 ) / 100
R = 6%

∴ Rate of interest is 6 %.

4. Explanation:

Let ratio be x.
Hence number of coins be 5x ,9x , 4x respectively.
Now given total amount = Rs.206
(0.50) (5x) + (0.25) (9x) + (0.10) (4x) = 206
2.5x + 2.25x + 0.4x = 206
5.15x = 206
we get x = 40
Number. of 50p coins = 5x
( 5 * 40 ) = 200
Number. of 25p coins = 9x
( 9 * 40 ) = 360
Number of 10p coins = 4x
( 4 * 40 )= 160

∴ The number of coins are 200, 360, 160.