Question

One third, one fourth, one fifth and one-seventh of the human population of North India which is less than five hundred, are all whole
numbers and their sum is exactly the population of South India. What is the human population of South India?​

Answer 1

Answer:

389 people live in South India

Step-by-step explanation:

3x4x5x7 = 420 which is less than 500

1/3 of 420 is 140

1/4 of 420 is 105

1/5 of 420 is 84

1/7 of 420 is 60

140+105+84+60 = 389

Answer 2

Answer:

Population of South India is 389.

Explanation:

Given,

one third of human population is less than 500

one fourth of human population is less than 500

one fifth of human population is less than 500

one seventh of human population is less than 500

let the population of North India be x

$\frac{1}{3} \times x < 500 \\ \frac{1}{4} \times x < 500 \\ \frac{1}{5} \times x < 500 \\ \frac{1}{7} \times x < 500$

take the lcm of 3,4,5,7 = 420

$\frac{1}{3} \times x < 500 = 140 < 500 \\ \frac{1}{4} \times x < 500 = 105 < 500 \\ \frac{1}{5} \times x < 500 = 84 < 500 \\ \frac{1}{7} \times x < 500 = 60 < 500$

now the sum of these will be equal to population of South India

so,

140 + 105 + 84 + 60 = 389

Population of South India = 389.