## Simplification Problems To Prepare For HCL Aptitude Tests

Below are three fraction based simplification problems which you can expect in HCL and all other companies aptitude tests.

**Question 1**

A man spent 5/16 of his age plus two as student, 1/40 plus 1 as a husband, 1/4 as a good politician and 3/40 as a father. And the remaining 6 years as a good grand father. Then the living days of the man is:

a) 72 b) 89 c) 80 d) 69

**Answer :**c)80

Solution :

Lets say his age is X.

So years spent as student = 5X / 16 + 2,

as Husband = X/4 + 1,

as Politician = X/4,

and as Father = 3X/40.

as Husband = X/4 + 1,

as Politician = X/4,

and as Father = 3X/40.

Remaining 6 years (as grandfather) = X - { 5X/16 + 2 + X/4 + 1 + X/4 + 3X/40}

i.e., 6 = X - { 5X / 16 + 2 + X / 4 + 1 + X / 4 + 3X / 40}

6 = X - [13X / 16 + 3 + 3X / 40]

6 = X - [71X / 80 + 3]

9X/80 = 9

X = 80.

Hence the age of the man is 80 years.

i.e., 6 = X - { 5X / 16 + 2 + X / 4 + 1 + X / 4 + 3X / 40}

6 = X - [13X / 16 + 3 + 3X / 40]

6 = X - [71X / 80 + 3]

9X/80 = 9

X = 80.

Hence the age of the man is 80 years.

**Question 2**

In a village, every weekend, 1/4 th of men and 1/6 th of women participate in the social activity. If the total number of participants is 75, out of them 25 are men then the total number of men and women in the village is:

a) 100 b) 200 c) 300 d) 400

**Answer :**d)400

Solution :

Number of men who participated in social activities = 25

Therefore, 1/4 th of the men = 25

Or, total number of men in the village = 100

Therefore, 1/4 th of the men = 25

Or, total number of men in the village = 100

Number of women who participated in social activities = 75 - 25 = 50

Therefore, 1/6 th of the women = 50

Or, total number of women in the village = 300

Hence the required answer is 300 + 100 = 400.

Therefore, 1/6 th of the women = 50

Or, total number of women in the village = 300

Hence the required answer is 300 + 100 = 400.

**Question 3**

A father has divided his properties in such a way that one-half of total properties goes to A, two-third of the remaining shared equally to B, C and D and the rest to E, F, G and H such they equally gets Rs.30,000 by their sharing property. Then the amount will D get is:

a) Rs.80,000 b) Rs.68,000 c) Rs.24,000 d) Rs.72,000

**Answer :**a) Rs.80,000

Solution :

A's share = 1/2

Then remaining = 1 - 1/2 = 1/2 ...(A)

Then remaining = 1 - 1/2 = 1/2 ...(A)

2/3 of this remaining 1/2 (as in eq A) goes to B,C and D.

Total share of B, C and D = 2/3 of 1/2 = 1/3

Total share of B, C and D = 2/3 of 1/2 = 1/3

Therefore, now remaining property = Total share of E,F,G and H

= value of (A) - total share of B,C and D

= 1/2 - 1/3 = 1/6

= value of (A) - total share of B,C and D

= 1/2 - 1/3 = 1/6

Then, E, F, G and H 's individual shares = (1/6) / 4 = 1/6 x 1/4 = 1/24

Given 1/24 = Rs.30,000

Then, total property amount = Rs.24 x 30,000 = Rs.7,20,000

Total share of B, C and D = 1/3 x 7,20,000

Then their individual share amount = (1/3 x 7,20,000) / 3 = Rs.80,000.

Hence D's share is Rs.80000.

Given 1/24 = Rs.30,000

Then, total property amount = Rs.24 x 30,000 = Rs.7,20,000

Total share of B, C and D = 1/3 x 7,20,000

Then their individual share amount = (1/3 x 7,20,000) / 3 = Rs.80,000.

Hence D's share is Rs.80000.