Question

The ratio of present ages of Priya and her mother is 2:9. At the time of the birth of
Priya age of mother was 28 years. What is the present age of Priya ?​

Answer 1

Answer:

The present age of Priya is 8 years old.

Step-by-step explanation:

Given :

Priya's mother was = 28 years old at the time of her birth.

Ratio of ages of Priya and her mother's present age = 2 : 9

To find :

Priya's present age

Solution :

$\textsf{\underline{\underline{Let the present age be - }}}$

• Priya as x
• Mother as x + 28

$\textsf{\underline{\underline{According to the question - }}}$

$\sf{\implies} \: x : x + 28 = 2 :9 \\ \\ \sf{\implies} \: \dfrac{x}{x + 28} = \dfrac{2}{9} \\ \\ \sf{\implies} \:9(x) = 2(x + 28) \\ \\ \sf{\implies} \:9x = 2x + 56 \\ \\ \sf{\implies} \:9x - 2x = 56 \\ \\ \sf{\implies} \:7x = 56 \\ \\ \sf{\implies} \:x = \dfrac{56}{7} \\ \\ \sf{\implies} \: x = 8$

Priya = 8 years old.

$\therefore$ The present age of Priya is 8 years old.

Answer 2

$\bold{\underline{\underline{\huge{\sf{AnsWer:}}}}}$

Present age of Priya is 8 years

$\bold{\underline{\underline{\large{\sf{StEp\:by\:stEp\:explanation:}}}}}$

GiVeN :

• The ratio of present ages of Priya and her mother is 2:9.
• At the time of the birth of
• Priya, age of mother was 28 years

To FiNd :

• Present age of Priya

SoLuTioN :

Let x be the common multiple of the ratio 2:9

Present age of Priya = 2x years

Present age of Mother = 9x years

$\sf{\underline{\underline{As\:Per\:ThE\:qUeStIoN:}}}$

• At the time of the birth ofPriya age of mother was 28 years.

This statement implies the difference between the age of Priya and her mother.

Constituting it mathematically,

$\leadsto$ $\sf{9x\:-\:2x\:=\:28}$

$\leadsto$ $\sf{7x\:=\:28}$

$\leadsto$ $\sf{x\:=\:{\dfrac{28}{7}}}$

$\leadsto$ $\sf{x\:=\:4}$

Substitute x = 4 in the ratio of present age of Priya.

Present age of Priya :

$\leadsto$$\sf{2x}$

$\leadsto$ $\sf{2\:\times\:4}$

$\leadsto$ $\sf{8}$

$\sf{\therefore{Present\:age\:of\:Priya\:=\:8\:years}}$

$\bold{\huge{\underline{VeRiFiCaTiOn:}}}$

Present age of Priya = 8 years

Present age of Mother :

Substitute x = 4 in the present age ratio of mother.

$\leadsto$ $\sf{9x}$

$\leadsto$ $\sf{9\:\times\:4}$

$\leadsto$ $\sf{36}$

$\sf{\therefore{Present\:age\:of\:Mother\:=\:36\:years}}$

Given that difference between the age of Priya and her mother at the time of Priya's birth was 28.

Let's check if the condition is satisfied.

$\leadsto$ $\sf{9x\:-\:2x\:=\:28}$

$\leadsto$ $\sf{36\:-\:8\:=\:28}$

$\leadsto$ $\sf{28\:=\:28}$

LHS = RHS

Hence Substained.