Question

the ages of reena and neema are in the ratio of 5%6 five year from now their ages will be in the ratio of 6%7 find their present age​

Answer 1

Answer:

Reena's and Neema's present age is 25 and 30 years respectively.

Step-by-step explanation:

Given that:

The present ages of Reena and Neema are in the ratio 5 : 6.

Five years after, their ages will be in the ratio of 6 : 7.

To Find:

Their present ages.

Let us assume:-

Present age of Reena and Neema be 5x and 6x respectively.

After 5 years:

• Reena's age = 5x + 5
• Neema's age = 6x + 5

According to the question:

$\sf{\longmapsto5x+5:6x+5=6:7}$

Writing the ratios in fraction,

$\sf{\longmapsto\dfrac{5x+5}{6x+5}=\dfrac{6}{7}}$

By cross-multiplication:

$\sf{\longmapsto7(5x+5)=6(6x+5)}$

Opening the brackets,

$\sf{\longmapsto35x+35=36x+30}$

Transposing variables to LHS, constants to RHS and changing their sign,

$\sf{\longmapsto35x-36x=30-35}$

Subtracting,

$\sf{\longmapsto-x=-5}$

$\sf{\longmapsto\not\!{-}x=\not\!{-}5}$

$\sf{\longmapsto x=5}$

Hence,

x = 5

Therefore,

Reena's present age = 5x = 5 × 5 = 25 years

Neema's present age = 6x = 6 × 5 = 30 years

• Reena's present age = 25years
• Neema's present age = 30 years.

Answer 2

Corrected question:

➦ The ages of reena and neema are in the ratio of 5:6 five year from now their ages will be in the ratio of 6:7 find their present age

Information given to us:

➦Ages of reena and Neema are in the ratio of 5:6

➦ Ratio of their ages after five years is 6:7

Need to be calculated:

➦ Present ages of reena and neema

Performing calculations:

We are assuming:

➦ Present age of Reema be 5x

➦ Present age of Neema be 6x

After 5 years ages of Reema and Neema would be,

➦ Reena age would be 5x + 5

➦ Neema age would be 6x + 5

Equation formed by noticing the question:

➦ Reena age : Neema age = Ratio of their ages after 5 years

Substituting values:

➦ 5x + 5 : 6x + 5 = 6:7

Now it would be,

➦ 5x + 5 / 6x + 5 = 6/7

Solving now,

➦ 7 (5x + 5) = 6 (6x + 5)

➦ 35x + 35 = 36x + 30

➦ 35 - 30 = 36x - 36x

➦ 5 = x

Or,

➦ x = 5

Finding out present age of Reena:

➦ Present age of Reena = 5x

➦ Present age of Reena = 5 × 5

➦ Present age of Reena = 25 years

Finding out present age of Neema:

➦ Present age of Neema = 6x

➦ Present age of Neema = 6 × 6

➦ Present age of Neema = 36 years

Conclusion:

➦ Present age of Neema is 36 years

➦ Present age of Reena is 25 years