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CAT 2001 — QA Question 20

3 Variable EquationsEasy

Every ten years the Indian government counts all the people living in the country. Suppose that the director of the census has reported the following data on two neighbouring villages Chota hazri and Mota hazri:

Chota hazri has 4,522 fewer males than Mota hazri.
Mota hazri has 4,020 more females than males.
Chota hazri has twice as many females as males.
Chota hazri has 2,910 fewer females than Mota hazri.
What is the total number of males in Chota hazri?

Answer & solution

  • A

    11264

  • B

    14174

  • 5632

  • D

    10154

Solution

Let a = no. of males in Chota hazri, b = no. of males in Mota hazri, x = no. of females in Chota hazri and y = no. of females in Mota hazri

∴ a + 4522 = b                               ...(i)

∴ y = b + 4020                              ...(ii)

∴ x = 2a                                        ...(iii)

∴ x = y – 2910                               ...(iv)

Using (iv), (ii)  and (iii), we have,

2a = b + 4020 – 2910

Substituting from (i), we have,

2a = a + 4522 + 4020 – 2910

a  = 5632

Hence, option (c).

CAT 2001 QA Q20: Every ten years the Indian government counts all the people living in the country. Suppose that the director o — Solution | TheCATExam