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Q.

Three numbers are in the ratio of 4: 5: 6. If the sum of the largest and the smallest is 55 more than the third, then the numbers are:

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a

44,55 and 66

b

55,66 and 77

c

None of these

d

33,44 and 55

answer is A.

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Detailed Solution

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We are given three numbers with the ratio 4:5:6 and the sum of the largest and smallest numbers is 55 more than the third.
Now, we have to determine the numbers using these two conditions.
So, using the first condition, i.e., the ratio between the three numbers, let the three numbers be 4x, 5x and 6x.
Now, using the second the condition, we can form an equation as follows,
6x+4x = 5x + 55
10x = 5x + 55
Subtracting 5x on both sides, we get,
10x – 5x = 5x - 5x + 55
5x=55
Dividing by 5 on both sides, we get,

5 x 5 = 555 x = 11

Now, we can find the numbers by substituting the value of x, as follows,
The largest number is,

6 x = 6 × 11 = 66

The smallest number is,

4 x = 4 × 11 = 44

The third number is,

5 x = 5 × 11 = 55

So, the numbers as per the given conditions are 44, 55 and 66.
Hence, the correct option is (1).

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