Home
Class 12
MATHS
Divide 28 into four parts in an A.P. so ...

Divide 28 into four parts in an A.P. so that the ratio of the product of first and third with the product of second and fourth is 8:15.

Text Solution

Verified by Experts

The correct Answer is:
4, 6, 8, 10
Let four member be a-3d,a-d,a+b,a+3d.
Here, 4a=28 or a=7
Also, `((a-3d)(a+d))/((a-d)(a+3d))=8/15`
or `15[a^(2)-3d^(2)-2ad]=8[a^(2)-3d^(2)+2ad]`
or `7(a^(2)-3d^(2))=46ad`
or `7(49-3d^(2))=46xx7xxd`
or `49-3d^(2)=46d`
`3d^(2)+46d-49=0`
or (d-1)(3d+49)=0
or d=1
Therefore, the required numbers are 4, 6, 8, 10.
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERICISE 5.3|9 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERICISE 5.4|13 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERICISE 5.1|3 Videos

  • PROBABILITY II

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

Similar Questions

Explore conceptually related problems

Divide 32 into four parts which are in A.P. such that the ratio of the product of extremes to the product of means is 7:15.

Divide 21 into three parts in A.P. such that the product of the first and second parts is 21.

A man divides Rs. 24000 among his four sons in such a way that the amounts received by the four sons are in A.P. The ratio of the product of the amounts received by the 1st and the 3rd sons to the product of the amounts received by 2nd and 4th sons is 7 : 15. Calculate the amounts received by each son.

Divide 24 into two parts such that their product is maximum.

Divide 24 into two parts such that their product is maximum.

Divide 56 into two parts, so that thrice of the first part becomes 48 more than one third of the second part.

Divide 5 into two parts such that the product of the square of one and the cube of the other may be the greatest possible.

There number are in A .P .whose sum is 6 and product of first and third number is 3 . Find the three numbers .

The sum of four integar in A.P is 24 and their product is 945. Find the numbers.

There are 3 positive whole numbers, the product of first and second number is 24, product of second and third number is 48 and that of first and third is 32: Let's calculate to find the three numbers.