Question

the present ages of reenu and Rohit are in the ratio of 3:5 after 10 years their ages will be 5:7. Find their present ages. with steps too please​

Answer 1

Given: The present ages of Reenu and Rohit are in the ratio of 3 : 5. & After 10 years their ages will be 5 : 7 respectively.

Need to find: Their present ages?

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❍ Let's say, that the present age of Reenu be 3x and present age of Rohit be 5x respectively.

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$\underline{\bigstar\:\boldsymbol{According\;to\;the\; Question\; :}}$⠀⠀

• After ten years, the age of Rohit and Reenu will be 5 : 7

☆ After 10 years, their ages —

• Reenu's age = (3x + 10) years
• Rohit's age = (5x + 10) years

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Therefore,

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$:\implies\sf\Bigg\{\dfrac{3x + 10}{5x + 10}\Bigg\} = \Bigg\{\dfrac{5}{7}\Bigg\}\\\\\\:\implies\sf 7\Big\{3x + 10\Big\} = 5\Big\{5x + 10\Big\}\\\\\\:\implies\sf 21x + 70 = 25x + 50\\\\\\:\implies\sf 21x - 25x = 50 - 70\\\\\\:\implies\sf -4x = -20 \\\\\\:\implies\sf x = \cancel\dfrac{20}{4} \\\\\\:\implies\underline{\pink{\boxed{\pmb{\frak{x = 5}}}}}\;\bigstar$

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$\underline{\bf{\dag} \:\mathfrak{So,\; their\; present\;Ages\: :}}$⠀⠀⠀⠀

• Reenu's present age, 3x = 3(5) = 15
• & Rohit's present age, 5x = 5(5) = 25

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$\therefore{\underline{\textsf{Hence, present ages of reenu and rohit is \textbf{15 years, 25 years} respectively.}}}$

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Answer 2

Given :-

the present ages of Reenu and Rohit are in the ratio of 3:5 after 10 years their ages will be 5:7.

To Find :-

Present ages

Solution :-

Let the present age of Reenu be 3a

Present age of Rohit be 5a

After 10 years

Present age of Reenu = 3a + 10

Present age of Rohit = 5a + 10

3a + 10/5a + 10 = 5/7

7(3a + 10) = 5(5a + 10)

21a + 70 = 25a + 50

70 - 50 = 25a - 21a

20 = 4a

20/4 = a

5 = a

Therefore

Present age of Reenu = 3a = 3(5) = 15 years

Present age of Rohit = 5a = 5(5) = 25 years