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The ratio of their age is 3:7.
Step-by-step explanation:
Given,
10 years ago, the ratio of two brothers was 1:4
After 14 years the ratio will be 4:7
To find the ratio of their present age.
Let,
10 years age their age was x and 4x
So, now their age is (x+10) and (4x+10)
14 years from now their age will be (x+10+14) and (4x+10+14)
That is x+24 and 4x+24
According to the problem,
x+24 : 4x+24 = 4:7
or,
or, 7(x+24) = 4(4x+24)
or, 7x+168 = 16x+ 96
or, 16x-7x = 168-96
or, 9x = 72
or, x = 8
Hence,
Their present age is (8+10) and (4×8+10) = 18 and 42
Hence,
The ratio of their age is 18:42 = 3:7