A) If a:b = 2:5 and b:c = 3:4, find (i) a:c(ii) a:b:c b) If x:y = 1:2 and y:z = 4:5, find (i) x:z(ii) x:y:z

A i. a:c=3:10

ii. a:b:c=2:5:10

B i. x:z=2:5

ii. x:y:z=2:4:5

Step-by-step explanation:

A.) If a:b = 2:5 and b:c = 3:4, find (i) a:c(ii) a:b:c

a:b=a/b=2/5

b:c=b/c=3/4

a/b*b/c=a/c

2/5*3/4=a/c

6/20=a/c

3/10=a/c

Therefore, a:c=3:10

a:b:c

a:b=2:5

b:c=3:4

b is common to both ratios

The value of b in the first ratio is 5 and b is 3 in the second ratio

Lets take the LCM of both values

LCM of 5 and 3=15

So, we will change the value of b in the first ratio and second ratio to 15

By doing this, we will multiply the whole first ratio by 3

We have, 6:15

We multiply the whole second ratio by 5

We have, 15:20

Therefore a:b:c=6:15:20

=2:5:10

B. If x:y = 1:2 and y:z = 4:5,

x:y=x/y=1:2

y:z=y/z=4:5

x/y*y/z=x/z

1/2*4/5=x/z

4/10=x/z

2/5=x/z

Therefore, x:z=2:5

x:y:z

x:y=1:2

y:z=4:5

y is common to both ratio

Take the LCM of y values in both ratio

LCM of 2 and 4 =4

So,we will change the value of y in the first and second ratio to 4

By doing this, we will multiply the whole first ratio by 2

We have, 2:4

We will also multiply the whole second ratio by 1

We have, 4:5

Therefore, x:y:z=2:4:5

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