Question

what number should be added to the number in the ratio 5 is to 6 so that the ratio becomes 8 is to 9 and the sum would term would be 51​

Answer 1

Answer:

24:27 are the no.s which are in the ratio 8:9. and the sum is 51.

24 is the third multiple of 8 and 27 is the third multiple of 9.

so multiplying 3 to 5 and 6 ,we get it is 15&18 respectively.

so subtract 15 from 24 we get 9.

so adding 9 in 5:6 to get 8:9

Answer 2

The value of number should be added to the number in the ratio 5 is to 6 so that the ratio becomes 8 is to 9. is 9.

Step-by-step explanation:

Given:

The ratio 5 is to 6 so that the ratio becomes 8 is to 9.

The sum would term would be 51​.

To Find:

The value of number should be added to the number in the ratio 5 is to 6 so that the ratio becomes 8 is to 9.

Solution:

Let q is multiplier.

As given,The ratio 5 is to 6 .

one number=5q

another number=6q

let  the number to be added= p

As given,the sum would term would be 51​.

$(5q+p) + (6q+p) = 51$

$11q+2p=51$   ------ equation no.01.

As given,the ratio becomes 8 is to 9.

$\frac{5q+p}{6q+p} =\frac{8}{9}$

$9(5q+p)=8(6q+p)$

$45q+9p=48q+8p$

$9p-8p=48q-45q$

$p=3q$

$q=\frac{p}{3}$ ------ equation no .02.

Putting the value of q from equation no.02 to equation no.01.  We get.

$11(\frac{p}{3} )+2p=51$

$11p+2p\times3=51\times3$

$11p+6p=153$

$17p=153$

$p=\frac{153}{17}$

 $p=9$  

Thus,the value of number should be added to the number in the ratio 5 is to 6 so that the ratio becomes 8 is to 9 is 9.

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