Find x: y: z given that and and .

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answer is A.

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Detailed Solution

Concept- Here x: y and y: z are given. We can find the combined ratio using the common variable

. o do this, the corresponding numbers must be equal in both proportions. Multiplying both numbers in a ratio by an integer does not change the ratio.
Useful formula:
If we multiply both numbers by the same integer, the ratio remains the same.
That is,

, for any m, n, a.
We are given that

and

.
We have to find x: y: z.
Here we can see that y is the same for both ratios.
so that you can use it to find ratios.
We know that a ratio does not change if we multiply both the numbers by the same integer.
In order for the number corresponding to y to be the same in both ratios, we can multiply the supplied ratios.
Now the numbers corresponding to y are 15 and 21 .
We can see that the least common multiple of these is 105, where

Consider 12: 15.
Multiplying both numbers by 7 we get, 84: 105
This gives,

Consider 21: 25.
Multiplying both numbers by 5 we get, 105: 125.
This gives,

Now we have,

and

.
Combining these two we get,

Hence, the correct option is (1) .

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