Question

The sum of digits of a two-digit number is 9. When the digits are reversed, the number decreases by 45. Find the changed number.

Answer 1

Let 2 numbers X and Y

So X + Y = 9....(1)

Original number 10X + Y

If number is reversed 10Y + X

Then 10X + Y = (10Y + X) - 45

9X = 9Y - 45

9X - 9Y = 45.....(2)

Solving (1) and (2)

X = 2 and Y = 7

So original number 10×(2) + 7 =27..

Answer 2

Answer:

$27$

Explanation:

Step : 1Let the digit at Unit place of a ne be ' $x^{\prime}$ & the digit at Terisplace be ' $y$'

$\therefore$ original no $=10 y+x$

AT $\theta$

$\begin{aligned}& x+y=9-(1) \\\text { New no }= & 10 x+y\end{aligned}$

$\begin{aligned}10 x+y & =10 y+x-45 \\10 x-x & =10 y-y-45 \\9 x & =9 y-45 \\45 & =9 y-9 x \\45 & =9(y-x)\end{aligned}$

$\begin{gathered}y-x=5 \\x+y=9 \\2 y=14 \\y=7 \\x+y=9 \\x=9-7=2\end{gathered}$

$\begin{aligned}\therefore \quad \text { New No }= & 10 x+y \\= & 10 \times 2+7 \\= & 20+7=27\end{aligned}$

Step : 2 In mathematics, the term "decreased" refers to taking a value's original value and subtracting a specified percentage from it. To accomplish this, we can either compute the value's percentage and then subtract it from the original value, or we can multiply the result by a percentage.

Step : 3Calculate the difference (reduction) between the two figures you are comparing in order to arrive at the % drop. Then, increase the result by 100 after dividing the decrease by the initial number.

Step : 4Decline and reduce: If you want to lessen something's size, amount, scope, or number, use the term "reduce." Using the term "decrease" suggests a gradual fall over time.

Example: You should eat less food that is high in calories if you want to lose weight and minimize your waistline.

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