Question

Populations of two villages X and Y are in the ratio of 5 : 7 respectively. If the population of village Y increases by 25000 and the population of village X remains unchanged the respective ratio of their populations becomes 25 :36. What is the population of village X ?

Answer 1

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Answer 2

Answer:

$\red {Population \: of \: village \: X }\green {=625000}$

Step-by-step explanation:

$Ratio \: of \: population \:of \: two \: villages\\X \:and \:Y = \frac{5}{7}$

$\implies 7X = 5Y$

$\implies Y = \frac{7X}{5} \: ---(1)$

/* According to the problem given,

If the population of village Y increases by 25000 and the population of village X remains unchanged the respective ratio of their populations becomes 25 :36 */

$\frac{X}{Y+25000} = \frac{25}{36}$

$\implies \frac{X}{\frac{7X}{5}+25000} = \frac{25}{36}\: [ From \: (1)]$

$\implies \frac{5X}{7X+125000} = \frac{25}{36}$

$\implies 36\times 5X = 25 \times (7X+125000)$

$\implies 180X = 175X + 3125000$

$\implies 180X - 175X = 3125000$

$\implies 5X = 3125000$

$\implies X = \frac{3125000}{5}$

$\implies X = 625000$

Therefore.,

$\red {Population \: of \: village \: X }\green {=625000}$

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