Question

Six years ago, Ram's age was four times Shyam's
age. Six years hence, Ram's age will be thrice
Shyam's age. After how many years from now will
their combined age be 150 years?
40
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Answer 1

Answer:

After 9 years the sum of their ages will be 150 year.

Step-by-step-explanation:

Let the required age of Ram before 6 year was a year.

So, present age of Ram should be ( a + 6 ) year.

Six years ago :

Ram's age = 4 x Shyam's age

a year = 4 x Shyam's age

a / 4 = Shyam age { 6 year ago }

= > Age of Ram after 6 year = present age + 6 year

= > Age of Ram after 6 years = ( a + 6 ) year + 6 year = ( a + 12 ) year.

After 6 years :

Ram's age = 3 x Shyam's age

( a + 12 ) year = 3 x Shyam's age

= > ( a + 12 ) year = 3[ Present age + 6 year ]

= > ( a + 12 ) year = 3[ ( Age before 6 year + 6 year ) + 6 year ]

= > a + 12 = 3[ a / 4 + 6 + 6 ]

= > a + 12 = 3( a + 48 ) / 4

= > 4a + 48 = 3a + 144

= > 4a - 3a = 144 - 48

= > a = 96

= > a = 96

Therefore, present age of Ram is 96 + 6 i.e. 102 year and Shyam is 96 / 4 + 6 year i.e. 30 year.

Let after x years the sum of their ages will be 150 :

= > Age of Ram after x year + age of Shyam after x year = 150 year

= > ( present age of Ram + x year ) + ( present age of Shyam + x year ) = 150 year

= > ( 102 + 30 + 2x ) = 150

= > 132 + 2x = 150

= > 2x = 18

= > x = 9

Hence after 9 years the sum of their ages will be 150 year.

Answer 2

Answer:

9 years

Step-by-step explanation:

Let the present ages of Ram and Shyam be r years and

s years respectively.

r − 6 = 4(s − 6) ⇒ r = 4s − 18

And r + 6 = 3(s + 6) ⇒ r = 3s + 12

∴ 4s − 18 = 3s + 12 ⇒ s = 30, r = 102

∴ their present combined age is 132 years. It has to increase

by 18 years to become 150 years. This will happen if the

age of each increases by 9 years