the ratio of a:b:c,when a:b =3:5 and b:c=6:7
Answers
Answer:
18 : 30 : 35 is a : b : c
Explanation:
These are the two ratios given to us:
- a : b = 3 : 5
- b : c = 6 : 7
We need to Find:
- a : b : c
[ We can see, b is common in the given two ratios, but it has a different value in each ratio i.e. 5 and 6. So, we can take any common multiple of 5 and 6 so that we can find a : b : c ]
[ For the ease of calculations, we will take the lowest common multiple. note that: taking any multiple will work. ]
LCM of 5 and 6
To find the LCM, we will prime factorise 5 and 6, then we will multiply the factors together, we'll take the common multiple ones.
5 = 1 × 5
6 = 1 × 2 × 3
LCM = 5 × 1 × 2 × 3 = 30
30 is the LCM of 5 and 6
a : b
⟹ 3 : 5
⟹ 3 × 6 : 5 × 6
⟹ 18 : 30 . . .( 1 )
b : c
⟹ 6 : 7
⟹ 6 × 5 : 7 × 5
⟹ 30 : 35 . . .(2)
[ Note that dividing or multiplying both the quantities in a ratio with the same number will not change the ratio. we are still comparing the same. ]
⟹ a : b :: b : c
⟹ a : b : c
[ Substituting values for a, b and c from equation ( 1 ) and equation (2) ]
⟹ 18 : 30 : 35
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