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Questions  >>  Olympiad-Math  >>  Class 5  >>  Number Sense

There are 3 numbers, the third one is the highest in value. The ratio of the third number to the second number is 6:1. The difference between the second and third number is 125 and the first and third number is 100. Find the sum of the three numbers

(A) 200 (B) 175 (C) 225 (D) 250

1 Answer

Let the three numbers be X, Y and Z.
Z: Y : : 6: 1 $\rightarrow$ Z = 6Y.
Difference between Z and Y is given as 125, i.e, Z - Y = 125.
Let us substitute Z = 6Y here $\rightarrow$ 6Y - Y = 125 $\rightarrow$ 5Y = 125 $\rightarrow$ Y = 25.
Now we can calculate Z = 6Y $\rightarrow$ 6 x 25 = 150.
Difference between Z and X is given as 100, i.e, Z - X = 100 $\rightarrow$ 150 - X = 100 $\rightarrow$ X = 150 - 100 = 50.
Therefore, we can solve this as follows: X+ Y + Z = 50 + 25 + 150 = 225.
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