Question

A mother divides rs.207 into three parts such that the amount are in



a.P and gives it to her three children. The profuct of the two least ammounts that the children had rs.4623 . Find the least amount

Answer 1

Answer:

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Answer 2

Given,

Total money divided by the mother into 3 parts = Rs. 207

The 3 divided amounts are in A P.

The product of the smaller two amounts = Rs. 4623

To find,

The smallest division of the amount.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the first term of the A.P. (smallest division amount) is a and its common difference is d.

Mathematically,

For an A.P. with the first term a and common difference d, its n-th term can be represented as;

n-th term of the A.P.= An = a + (n-1)d And, the sum of its first n terms is;

Sn = n/2{2a + (n-1)d}

Now, according to the question,

A1 + A2 + A3 = 207

=> S3 = 207

=> 3/2(2a + 2d) = 207

=> 3(a+d)=207

=> (a+d)=69

(a+d)=69{Equation-1}

Also,

A1 × A2 = 4623

=> a(a + d) = 4623

=> a × 69 = 4623 (according to equation-1)

=> a = 67

=> first term of the A.P. = smallest division amount = Rs. 67

Hence, the smallest division of the amount is equal to Rs. 67.