Question

The sum of four numbers is 253. The ratio of the first to the second is 2 : 3. The ratio of the second to the third is 5 : 6. The ratio of the third to the fourth is 8 : 9. What is the average of the second and the third number?

Answer 1

Let the 1stno. A = X
2nd no.= B , 3rd no.= C , 4th no. = D

A: B =2:3
A/B = 2/3
x/B =2/3
B= 3x/2

B:C=5:6
(3x/2)/ C= 5/6
C=( 6×3x)/2×5= 9x/5
C= 9x/5

C:D= 8:9
9x/5/ D = 8/9
D= (9x×9)/8×5= 81x/40
D= 81x/40

A+B+C+D= 253. (GIVEN)
x+ 3x/2+9x/5+81x/40

Lcm = 40

(40x+ 60x+ 72x+81x)/40= 253

253x= 253×40

X= (253×40)/253= 40

Ist no.(A)= X= 40

2no.(B)= 3x/2=( 3 × 40)/2= 60

3rd no.(C)= 9x/5 = (9×40)/5= 72

4th no.(D)= 81x/40=( 81×40/)/40= 81
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Average of numbers= sum of observations/ total no. Of observations

Average of 2nd no. & 3rd no.= (60+72)/2= 132/2= 66
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Average of 2nd no. & 3rd no.=66
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Hope this will help you......