Math
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# 6. If a : b = 2 : 3 and b: c = 4:5, t a:b:c the ratio is​

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Let us first consider the value of b.

It is given that a: b = 2:3 and b: c = 4:5. Thus, LCM of 3 and 4 is 12. Therefore, we need to multiply the first ratio by 4 and the second ratio by 3.

⇒a: b = 4(2): 4(3) = 8:12

⇒b: c=3(4):3(5) = 12:15

Now, as the value of b is common across the two ratios, we can combine them.

Therefore, a:b:c=8:12:15.

Now, we shall make the value of c common.

The ratios with us are a: b: c= 8:12:15 and c: d=6:7.

LCM of 15 and 6 is 30. Therefore, we need to multiply the first ratio by 2 and the second ratio by 5.

⇒ a:b:c=2(8): 2(12): 2(15) = 16:24:30

⇒c: d = 5(6): 5(7) = 30:35

Now, as the value of c is common across the two ratios, we can combine them.

Therefore a:b:c:d=16:24:30:35

Note: It is to be noted that the multiplying the antecedent and consequent of the ratio with the same number does not change the value of the ratio.

I hope this will helpful to you

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