Question

the ages of rita and geeta ratio of 5:7. four years now their ages will be in the ratio 3:4. their present ages are _______

Answer 1

Answer: THEIR PRESENT AGES ARE 20 AND 28 RESPECTIVELY.

Step-by-step explanation: LET THE PRESENT AGES OF RITA AND GEETA BE 5X AND 7X RESPECTIVELY.

FOUR YEARS FROM NOW THEIR AGES WILL BE 5X+4 AND 7X+4.

NOW, THE EQUATION WILL BE

5X+4/7X+4 = 3/4

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NOW SOLVE THIS!

Answer 2

Answer :

The age of Rita is 20 years and that of Geeta is 28 years

Given :

• The ages of Rita and Geeta are in the ratio of 5:7
• 4 years later from now their ages will be in the ratio 3:4

To Find :

• The present ages of Rita and Geeta

Solution :

Let us consider the ages of Rita and Geeta be x years and y years respectively

According to First condition :-

$\implies\sf{\dfrac{x}{y}= \dfrac{5}{7}}\\\\ \implies\sf{x=\dfrac{5}{7}\times y.......(1)}$

By the second condition :-

$\implies\sf{\dfrac{x+4}{y+4}= \dfrac{3}{4}}\\\\ \implies\sf{\dfrac{\dfrac{5y}{7}+4}{y+3}= \dfrac{3}{4}}\\\\ \implies \sf{ \dfrac{4(5y + 28)}{7}=3\times(y+4)}\\\\ \sf{\implies4\times(5y +28) = 7\times3\times(y +4) }\\\\ \sf{\implies 20y + 112 = 21y + 84}\\\\ \sf{\implies 21y - 20y = 112-84}\\\\ \implies\bf{y = 28}$

Thus , age of Geeta is 28 years

Now putting the value of y in (1) :

$\sf{\implies x = \dfrac{5}{7}\times28}\\\\ \sf{\implies x = 5 \times 4}\\\\ \bf{\implies x = 20}$

Thus , the age of Rita is 20 years .