Aptitude Solved Problems

1. The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder person?

Answer: 30 years

Explanation:

Let present age of the elder person = x

Present age of the younger person = ( x - 16 )

By given condition ,

( x - 6 ) = 3 * ( x - 16 - 6 )

( x - 6 ) = 3 * ( x - 22 )

( x - 6 ) = ( 3x - 66 )

2x = 60

x = ( 60 / 2 )

x = 30

∴ Present age of the elder person is 30 years.

2. A rectangular field has to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?

Answer: 88 feet

Explanation:

Area of the field = 680 sq.feet

length = 20 feet.

( length * breadth ) = 680 sq.feet

( 20 * breadth ) = 680

Breadth = ( 680 / 20 )

Breadth = 34 feet

Length of fencing = ( length + ( 2 * breadth ) )

= ( 20 + ( 2 * 34 ) )

= ( 20 + 68 )

= 88 feet

∴ Area to be fenced is 88 feet.

3. There are two divisions A and B of a class, consisting of 36 and 44 students respectively. If the average weight of divisions A is 40 kg and that of division B is 35 kg. What is the average weight of the whole class?

Answer: 37.25 kg

Explanation:

Given that,

Average weight of divisions A is 40 kg.

Average weight of divisions B is 35 kg.

Total weight of students in division A = ( 36 * 40 )

Total weight of students in division B = ( 44 * 35 )

Total students = ( 36 + 44 )

= 80

Average = ( Total weight of students in division A + Total weight of students in division B ) / ( Total students )

= ( 36 * 40 ) + ( 44 * 35 ) / 80

= ( 9 * 40 ) + ( 11 * 35 ) / 20

= ( 9 * 8 ) + ( 11 * 7 ) / 4

= ( 72 + 77 ) / 4

= ( 149 / 4 )

= 37.25

∴ Average weight of the whole class is 37.25 kg.

1. The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder person?

Answer: 30 years

Explanation:

Let present age of the elder person = x

Present age of the younger person = ( x - 16 )

By given condition ,

( x - 6 ) = 3 * ( x - 16 - 6 )

( x - 6 ) = 3 * ( x - 22 )

( x - 6 ) = ( 3x - 66 )

2x = 60

x = ( 60 / 2 )

x = 30

∴ Present age of the elder person is 30 years.

2. A rectangular field has to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?

Answer: 88 feet

Explanation:

Area of the field = 680 sq.feet

length = 20 feet.

( length * breadth ) = 680 sq.feet

( 20 * breadth ) = 680

Breadth = ( 680 / 20 )

Breadth = 34 feet

Length of fencing = ( length + ( 2 * breadth ) )

= ( 20 + ( 2 * 34 ) )

= ( 20 + 68 )

= 88 feet

∴ Area to be fenced is 88 feet.

3. There are two divisions A and B of a class, consisting of 36 and 44 students respectively. If the average weight of divisions A is 40 kg and that of division B is 35 kg. What is the average weight of the whole class?

Answer: 37.25 kg

Explanation:

Given that,

Average weight of divisions A is 40 kg.

Average weight of divisions B is 35 kg.

Total weight of students in division A = ( 36 * 40 )

Total weight of students in division B = ( 44 * 35 )

Total students = ( 36 + 44 )

= 80

Average = ( Total weight of students in division A + Total weight of students in division B ) / ( Total students )

= ( 36 * 40 ) + ( 44 * 35 ) / 80

= ( 9 * 40 ) + ( 11 * 35 ) / 20

= ( 9 * 8 ) + ( 11 * 7 ) / 4

= ( 72 + 77 ) / 4

= ( 149 / 4 )

= 37.25

∴ Average weight of the whole class is 37.25 kg.

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