Question

The present ages of Amit and Sumit are in the ratio 11:8. After eight years, the ratio of their ages will be 5: 4. Find their present ages.

Answer 1

Answer:

11x+8+8x+8=5/4

19x+16=5/4

19x=5/4-64/4

19x=-59

x=-59/19

x=3.12 round off value

11x=3.12×11=34.32

8x=3.12×8=24.96

round off value

Amit =34 years

Sumit= 25 years

Answer 2

Given :

• Present ages of Amit and Sumit are in the ratio 11:8 .After eight years the ratio of their ages will be 5:4 .

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

To Find :

• Find the present age.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Solution :

➺ Present age of Amit and Sumit are in the ratio 11:8 .Hence ,

$\large{\blue{\bigstar}} \: {\underline{\red{\sf{ \dfrac{Amit}{Sumit} = \dfrac{11x}{8x}}}}}$

➺ After 8 years their ages will be in the ratio 5:4 .Hence ,

$\large{\blue{\bigstar}} \: {\underline{\red{\sf{ \dfrac{11x + 8}{8x + 8} = \dfrac{5}{4}}}}}$

$\qquad{━━━━━━━━━━━━━━━}$

~ Now let's Cross Multiply :

${\longmapsto{\qquad{\sf{ 4(11x + 8) = 5(8x + 8) }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ 44x + 32 = 40x + 40 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ 44x - 40x = 40 - 32}}}} \\ \\ \ {\longmapsto{\qquad{\sf{ 4x = 8 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ x = \cancel\dfrac{8}{4}}}}} \\ \\ \ {\qquad{\sf{ Value \: of \: x \: = {\underline{\underline{\color{green}{\sf{ 2 }}}}}}}}$

$\qquad{━━━━━━━━━━━━━━━}$

~ Present ages of Amit and Submit :

$\qquad{\pink{\leadsto{\underline{\underbrace{\color{darkblue}{\sf{ Age \: of \: Amit \: = 11x = 11 \times 2 = 22 \: years }}}}}}}$

$\qquad{\pink{\leadsto{\underline{\underbrace{\color{darkblue}{\sf{ Age \: of \: Sumit = 8x = 8 \times 2 = 16 \: years }}}}}}}$

$\qquad{━━━━━━━━━━━━━━━}$

Therefore :

❝ Age of Amit is 22 years and age of Sumit is 16 years. ❞

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬