Mathematics
A number of three digits has the hundred digit 4 times the unit digit and the sum of three digits is 14. If the three digits are written in the reverse order, the value of the number is decreased by 594. Find the number.
Linear Equations
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Answer
Let the digit at ten's place be x and unit's place be y.
Then according to question,
Digit at hundred's place = 4y.
Number = 100 × 4y + 10 × x + y = 400y + 10x + y = 401y + 10x.
Reversing the number becomes = 100 × y + 10 × x + 4y = 100y + 10x + 4y = 104y + 10x.
Given, sum of digits = 14.
∴ 4y + x + y = 14
⇒ x + 5y = 14 ……(i)
According to second condition,
⇒ 401y + 10x = 104y + 10x + 594
⇒ 401y - 104y + 10x - 10x = 594
⇒ 297y = 594
⇒ y = 2.
Substituting value of y in (i) we get,
⇒ x + 5(2) = 14
⇒ x + 10 = 14
⇒ x = 4.
Number = 100 × 4y + 10 × x + y = 100 × 4(2) + 10 × 4 + 2 = 800 + 40 + 2 = 842.
Hence, number = 842.
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