Question

In a group of people, 28% of the members are young while the rest are old. If 65% of the members are literates, and 25% of the literates are young, then the percentage of old people among the illiterates is nearest to

• A. 62
• B. 55
• C. 66
• D. 59

Answer 1

The Correct Option is C

To solve this problem, follow these steps:

Step 1: Young and Old Distribution

28% of the members are young. 
Hence, percentage of old members is: \[ 100\% - 28\% = 72\% \]

Step 2: Literates and Illiterates

65% are literates. 
Therefore, percentage of illiterates is: \[ 100\% - 65\% = 35\% \]

Step 3: Young Literates

25% of the literates are young: \[ 25\% \times 65\% = 16.25\% \]

Step 4: Old Literates

\[ 65\% - 16.25\% = 48.75\% \]

Step 5: Young Illiterates

Total young = 28%, so: \[ 28\% - 16.25\% = 11.75\% \]

Step 6: Old Illiterates

\[ 35\% - 11.75\% = 23.25\% \]

Step 7: Final Calculation

Percentage of old people among illiterates: \[ \frac{23.25}{35} \times 100 \approx 66.43\% \]

 Final Answer:

The percentage of old people among the illiterates is approximately 66%.

Answer 2

Among the total population, 28% are young and 72% are old.

Overall, 35% of the population is illiterate and 65% is literate.

Step 1: Illiterate and Literate Young Population

11.75% of the population are young illiterate.

Young literate population = \( \frac{1}{4} \times 65\% = 16.25\% \)

Step 2: Illiterate Old Population

Total illiterate population = 35% 
Illiterate young = 11.75% 
Therefore, illiterate old population = \( 35\% - 11.75\% = 23.25\% \)

Step 3: Percentage of Illiterates who are Old

Now, out of the total illiterate group (35%), the proportion that is old: \[ \frac{23.25}{35} \times 100 \approx 66.43\% \]

 Final Answer:

Approximately 66% of the illiterate population are old.