Aptitude Solved Problems

Aptitude Solved Problems
1. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

Answer: 25200
Explanation:
Number of ways of selecting 3 consonants from 7
= 7C3
Number of ways of selecting 2 vowels from 4
= 4C2
Number of ways of selecting 3 consonants from 7 and 2 vowels from 4
= 7C3 * 4C2
= ( 7 * 6 * 5 ) / ( 3 * 2 * 1 ) * ( 4 * 3) / ( 2 * 1 )
= 210
It means we can have 210 groups where each group contains total 5 letters (3 consonants and 2 vowels).
Number of ways of arranging 5 letters among themselves
= 5! = ( 5 * 4 * 3 * 2 * 1 )
= 120
Hence, required number of ways
= ( 210 * 120 )
= 25200
∴ Required number of ways are 25200

2. A man can row 6 Kmph in still water. If the velocity of the current is 2 Kmph and it takes him 2 hours to row to a place and come back. Find the distance of the place?

Answer: 5.33 km
Explanation:
Speed downstream = ( 6 + 2 ) km / hr
= 8 km / hr
Speed upstream = ( 6 - 2 ) km / hr
= 4 km / hr
Let the required distance be x km
( x / 8 ) + ( x / 4 ) = 2
( x + 2x ) / 8 = 2
3x = 2 * 8
3x = 16
x = 16 / 3
x = 5.33 km
∴ Distance = 5.33 km

3. A shopkeeper bought 600 apples and 400 papaya. He found 15% of apple and 8% of papaya were rotten. Find the percentage of fruits in good condition.

Answer: 87.8 %
Explanation:
Total number of fruits shopkeeper bought = 600 + 400
= 1000
Number of rotten apple = 15 % of 600
= ( 15 / 100 ) * 600
= 15 * 6
= 90
Number of rotten papaya = 8 % of 400
= ( 8 / 100 ) * 400
= 8 * 4
= 32
∴ Total number of rotten fruits = 90 + 32 = 122
∴ Number of fruits in good condition = 1000 - 122
= 878
Required Percentage of fruits in good condition
= ( ( 878 / 1000 ) * 100 ) %
= ( 87800 / 1000 ) %
= ( 878 / 10 ) %
= 87.8 %
∴ 87.8 % fruits are in good condition.