Question

Every 10 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?

• A. 11,264
• B. 14,174
• C. 5,632
• D. 10,154

Hint:

Translate verbal relationships into equations, then solve systematically by substitution.

Answer 1

The Correct Option is A

Let $M_c$ = males in Chota Hazri, $F_c$ = females in Chota Hazri, $M_m$ = males in Mota Hazri, $F_m$ = females in Mota Hazri.
From data: 1. $M_c = M_m - 4522$
2. $F_m = M_m + 4020$
3. $F_c = 2M_c$
4. $F_c = F_m - 2910$
From (3) and (4): $2M_c = M_m + 4020 - 2910 = M_m + 1110$. From (1): $M_c = M_m - 4522 \Rightarrow 2(M_m - 4522) = M_m + 1110 \Rightarrow 2M_m - 9044 = M_m + 1110 \Rightarrow M_m = 10154$. Then $M_c = 10154 - 4522 = 11264$.