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Question
Two numbers are in the ratio 4 : 7. If thrice the larger be added to twice the smaller, the sum is 59. Find the numbers.
Sum
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Solution
Given,
Two numbers are in the ratio 4 : 7.
`y/x = 4/7`
`=> y = (4x)/7` ...(1)
If thrice the larger be added to twice the smaller, the sum is 59.
3x + 2y = 59
`3x + 2 xx (4x)/7 = 59`
`3x + (8x)/7 = 59`
`=> (29x)/7 = 59`
`=> x = (59xx7)/29`
`x = 14 7/29`
`y = 4/7 xx 14 7/29`
`4/7 xx 413/29`
`= (4 xx 59)/29`
`= 8 4/29`
Hence, numbers are `= 8 4/29` and `14 7/29`
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