Question

ages of Ram and Venkat are in the ratio of 2:3 ages of Venkat and kamal are in the ratio of 4:5.Sum of the ages of Ram and Kamal 46 yrs. What is the difference between the ages of Ram and Venkat
a) 6yrs b)7yrs c) 8yrs d) 9yrs e)12yrs ​

Answer 1

Please refer to above attachment for your answer

OPTION E (12 YRS)

AFTER ROUND OFF

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Answer 2

Answer:

• The difference between Ram's age and Venkat's age is 8 years.

Step-by-step explanation:

Given that:

• Ages of Ram and Venkat are in the ratio of 2 : 3.
• Ages of Venkat and Kamal are in the ratio of 4 : 5.
• Sum of ages of Ram and Kamal is 46 years.

To Find:

• Difference between the ages of Ram and Venkat.

Solution:

$\sf{\circ\;\dfrac{Ram's\;age}{Venkat's\;age}=\dfrac{2}{3}}$

$\sf{\circ\;\dfrac{Venkat's\;age}{Kamal's\;age}=\dfrac{4}{5}}$

As Venkat's age is not same in both the ratios, so we have to take the LCM of 3 and 4 to make both the ratios with Venkat's age same.

• LCM of 3 and 4 = 3 × 4 = 12

Now,

$\sf{\dfrac{Ram's\;age}{Venkat's\;age}=\dfrac{2}{3}=\dfrac{2\times4}{3\times4}=\dfrac{8}{12}}$

$\sf{\dfrac{Venkat's\;age}{Kamal's\;age}=\dfrac{4}{5}=\dfrac{4\times3}{5\times3}=\dfrac{12}{15}}$

Now as in both the ratios Venkat's age is same, we can say that,

• Ages of Ram, Venkat and Kamal are in the ratio 8 : 12 : 15.

Let us assume:

• Age of Ram and Kamal be 8x and 15x respectively.

According to the question:

$\sf{\longmapsto8x+15x=46}$

Adding

$\sf{\longmapsto23x=46}$

Transposing 23 from LHS to RHS,

$\sf{\longmapsto x=\dfrac{46}{23}}$

Dividing,

$\sf{\longmapsto x=2}$

Therefore,

• Ram's age = 8x = 8 × 2 = 16 years
• Venkat's age = 12x = 12 × 2 = 24 years
• Kamal's age = 15x = 15 × 2 = 30 years

Finding difference the ages of Ram and Venkat:

$\sf{\dashrightarrow(24-16)\;years}$

$\sf{\dashrightarrow8\;years}$

Hence,

• Difference between the ages of Ram and Venkat is 8 years.

Therefore,

• Correct option is: Option - C