Question

# Four years back in time, a father was 3 times as old as his son then was. 8 years later father will be 2 times as old as his son will then be. Find the ages of son and father.

Hint:

### let present ages of son is x years and present age of father is y years

Find both the ages 4 years back and apply the condition.

Find both ages after 8 yrs and apply the condition.

Solve the two equation to get the age of son and father.

## The correct answer is: 40 years .

### Ans :- Age of Son is 16 years and Age of father is 40 years .

Explanation :-

Step 1:- frame the equations from the given set of conditions .

let present ages of son is x years and present age of father is y years

Fours years back, age of son = x-4

Fours years back, age of father = y-4

Four years back in time, a father was 3 times as old as his son then was

—Eq1

After 8 years, age of son = x+8

After 8 years, age of father = y+8

8 years later father will be 2 times as old as his son will then be

— Eq2

Step 2:- find x by eliminating y

Doing Eq1-Eq2 to eliminate x

∴ x= 16

Step 3:- substitute x=16 in Eq2.

∴ y = 40

∴ The present age of son =x=16 years and present age of father = 40 years

### Related Questions to study

### A number which is formed by two digits is 3 times the sum of the digits. While interchanging the digits it is 45 more than the actual number. Find the number.

### A number which is formed by two digits is 3 times the sum of the digits. While interchanging the digits it is 45 more than the actual number. Find the number.

### The gas mileage M (s), in miles per gallon, of a car traveling s miles per hour is modeled by the function below, where .

According to the model, at what speed, in miles per hour, does the car obtain its greatest gas mileage?

**Note:**

We could have also used the first derivative test to find the local

maxima. We need to find critical points and then check whether the

function is increasing or decreasing on either side of the critical

point. If the function is increasing , i. e ., on the left side

and the function is decreasing, i. e ., on the right hand side, then we say that is a local maxima.

### The gas mileage M (s), in miles per gallon, of a car traveling s miles per hour is modeled by the function below, where .

According to the model, at what speed, in miles per hour, does the car obtain its greatest gas mileage?

**Note:**

We could have also used the first derivative test to find the local

maxima. We need to find critical points and then check whether the

function is increasing or decreasing on either side of the critical

point. If the function is increasing , i. e ., on the left side

and the function is decreasing, i. e ., on the right hand side, then we say that is a local maxima.

### Given a rectangle ABCD, where AB = (4y-z) cm, BC = (y+4) cm, CD = (2y+z+8) cm, DA = 2z cm. Find y and z

### Given a rectangle ABCD, where AB = (4y-z) cm, BC = (y+4) cm, CD = (2y+z+8) cm, DA = 2z cm. Find y and z

### Find the volume of a right circular cylinder of length 80 cm and diameter of the base 14 cm.

### Find the volume of a right circular cylinder of length 80 cm and diameter of the base 14 cm.

### Find the area of the polygon in the given picture, cm,

### Find the area of the polygon in the given picture, cm,

### A man bought 3 paise and 5 paise denomination stamps for Rs 1.00. In total he bought 22 stamps. Find out total number of 3 paise stamps bought by him.

### A man bought 3 paise and 5 paise denomination stamps for Rs 1.00. In total he bought 22 stamps. Find out total number of 3 paise stamps bought by him.

### A ball pen costs Rs 3.50 more than pencil. Adding 3 ball pens and 2 pencils sum up to Rs 13. Taking y and z as costs of ball pen and pencil respectively. Write down 2 simultaneous equations in terms of y and z which satisfy the above statement. Find out the values of y and z.

### A ball pen costs Rs 3.50 more than pencil. Adding 3 ball pens and 2 pencils sum up to Rs 13. Taking y and z as costs of ball pen and pencil respectively. Write down 2 simultaneous equations in terms of y and z which satisfy the above statement. Find out the values of y and z.

### In a town there are 2 brothers namely Anand and Suresh. Adding 1/3 rd anand’s age and suresh age would sum up to 10. Also adding Anand’s age together with 1⁄2 of suresh age would sum up to 10. Find Anand and Suresh ages.

### In a town there are 2 brothers namely Anand and Suresh. Adding 1/3 rd anand’s age and suresh age would sum up to 10. Also adding Anand’s age together with 1⁄2 of suresh age would sum up to 10. Find Anand and Suresh ages.

### From a cylindrical wooden log of length 30 cm and base radius 72 cm, biggest cuboid of square base is made. Find the volume of wood wasted?

### From a cylindrical wooden log of length 30 cm and base radius 72 cm, biggest cuboid of square base is made. Find the volume of wood wasted?

### Find the area of the figure.

.

### Find the area of the figure.

.

The system of equations above is graphed in the xy -plane. At which of the following points do the graphs of the equations intersect?

**Note:**

We can solve the equations by other methods too, but the method of substitution is most suitable here. Also, instead of solving

by middle term factorisation, we could also use the quadratic formula, which is given by

Where the standard form of equation is

The system of equations above is graphed in the xy -plane. At which of the following points do the graphs of the equations intersect?

**Note:**

We can solve the equations by other methods too, but the method of substitution is most suitable here. Also, instead of solving

by middle term factorisation, we could also use the quadratic formula, which is given by

Where the standard form of equation is