Question

Ratio of present age of Roman and
Calibri is 5:7 and Calibri and Arial is
2:1. After 12 years, the ratio of their
age becomes 16 : 20 : 13. What was
their average age of 5 years ago?
A 15.66 years B. 15.25 years
C. 14.26 years
D. 18.29 years
E. 16.25 years​

Answer 1

Answer:

Option A

Step-by-step explanation:

Given :-

Ratio of present age of Roman and

Calibri is 5:7 and Calibri and Arial is

2:1. After 12 years, the ratio of their

age becomes 16 : 20 : 13.

To find :-

What was their average age of 5 years ago?

Solution:-

Given that

Ratio of present ages of Roman and Calibri = 5:7

R : C = 5 : 7

=> R/C = 5/7

=> R/C = (5/7)×(2/2)

=> R/C = (5×2)/(7×2)

=> R/C = 10/14

=> R :C = 10 : 14 --------(1)

Ratio of present ages of Cibri and Arial = 2:1

=> C : A = 2:1

=> C/A = 2/1

=> C/A = (2/1)×(7/7)

=> C/A = (2×7)/(1×7)

=> C/A = 14/7

=> C : A = 14 : 7 -------------(2)

From (1)&(2)

R : C = 10 : 14

C : A = 14 : 7

__________________

R : C : A = 10 : 14 : 7

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The ratio of the present ages of Roman , Calibri and Arial = 10 : 14 : 7

Let the present age of Roman = 10 X years

After 12 years , Age of Roman = (10X+12) years

Let the present age of Calibri = 14X years

After 12 years ,Age of Calibri = (14X+12) years

Let the present age of Arial = 7X years

After 12 years ,Age of Arial = (7X+12) years

Their ratio = (10X+12):(14X+12):(7X+12)

According to the given problem

After 12 years, the ratio of their

age becomes 16 : 20 : 13.

=> (10X+12):(14X+12):(7X+12) = 16 : 20 : 13.

Consider

(10X+12):(14X+12) = 16:20

=> (10X+12)/(14X+12)=16/20

=> (2)(5X+6)/(2)(7X+6) = 4/5

=> (5X+6)/(7X+6) = 4/5

On applying cross multiplication then

=> 5(5X+6) = 4(7X+6)

=> 25X+30 = 28X+24

=> 28X-25X = 30-24

=> 3X = 6

=>X = 6/3

=> X = 2

Now

The present age of Roman = 10 X years

=> 10(2)=20 years

The present age of Calibri = 14X years

=> 14(2)=28 years

The present age of Arial = 7X years

=> 7(2 ) = 14 years

Now,

5 years ago their ages was (20-5),(28-5),(14-5) years

=> 15 years , 23 years , 9 years

Average of the their ages

= Sum of their ages/ Number of people

= (15+23+9)/3

= 47/3

= 15.66 years

Answer:-

The average of their ages 5 years ago = 15.66 years

Used formulae:-

• a:b can be written as a/b
• Average= Sum of all observations/Number of all observations