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# the result of dividing a number by the number with the digits reversed is 1¾. if the sum of the digits is 12, the number is

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## The result of dividing the number of two digits by the number with digits reversed is 1 If the sum o...

Free solutions for M L Aggarwal - Understanding ICSE Mathematics - Class 9 Chapter 7 - Problems on Simultaneous Linear Equations Problems on Simultaneous Linear Equations Exercise 6 question 26. These explanations are written by Lido teacher so that you easily understand even the most difficult concepts ## ML Aggarwal Solutions Class 9 Mathematics Solutions for Problems on Simultaneous Linear Equations Exercise 6 in Chapter 6 - Problems on Simultaneous Linear Equations

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The result of dividing the number of two digits by the number with digits reversed is 1¾. If the sum of digits is 12, find the number.

Let’s consider the digit at tens place as x

And let the digit at unit place be y

The number is 10 × x + y × 1 = 10x + y

So, reversing the number = 10 × y + x × 1 = 10y + y

Then according to the first condition given in the problem, we have

(10x + y)/ (10y + x) = 1¾

(10x + y)/ (10y + x) = 7/4

4 (10x + y) = 7 (10y + x)

40x + 4y = 70y + 7x

40x – 7x – 70y + 4y = 0

33x – 66y = 0 x – 2y = 0 … (i)

And according to the second condition of the given problem, we have

x + y = 12 … (ii)

From equation (i) and (ii), we have

x + y = 12 x – 2y = 0 (-)—(+)—(-) 3y = 12 y = 12/3 y = 4

On substituting the value of y in (i), we have

x – 2(4) = 0 x = 8

Therefore, the number is 10 x 8 + 4 = 84.

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## The result of dividing a number of two digits by the number with the digits reversed is 5 6 . If the difference of digits is 1, find the number.

Click here👆to get an answer to your question ✍️ The result of dividing a number of two digits by the number with the digits reversed is 5 6 . If the difference of digits is 1, find the number. The result of dividing a number of two digits by the number with the digits reversed is

Question 6 5 ​

. If the difference of digits is 1, find the number.

Let a number be 10x+y

Medium Open in App Solution Verified by Toppr

Reversed number =10y+x

Thus, 10y+x 10x+y ​ = 6 5 ​ 60x+6y=50y+5x 55x=44y 5x=4y⟶(1) also, x−y=−1⟶(2)

on solving, we get x=4 and y=5 so, Number is 10x+y=45

102 26

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## The result of dividing a number of two digits by the number with the digits reversed is 7/4. If the sum of the digit is 12, what is the number?

Answer (1 of 4): Let the unit digit is x. The ten's digit =(12 - x) [ because the sum of the digits of the two digit number is 12]. The value of the two digit number = 10 . (12 - x ) +x = 120 -10 x + x = 120 - 9x ———(1) The value of the two digit number with unit and ten's digit interchanged = ... The result of dividing a number of two digits by the number with the digits reversed is 7/4. If the sum of the digit is 12, what is the number?

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Let the unit digit is x. The ten's digit =(12 - x) [ because the sum of the digits of the two digit number is 12].

The value of the two digit number = 10 . (12 - x ) +x = 120 -10 x + x = 120 - 9x ———(1)

The value of the two digit number with unit and ten's digit interchanged = 10 x + (12 - x) = 9 x + 12 —-(2)

According to the statement of the problem the division of the original number by the new number obtained by interchanging the position of the unit and ten's digit is 7/4, is

(120 - 9 x)/(9 x + 12) = 7/4

Simplifying we get

480 - 36 x = 63 x + 84

==> 99 x = 396 or x = 4.

Therefore, the unit's digit

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Are there any two 4-digit numbers that when reversed, become a 2-digit number?

Avinash Nayak 3y

Let the digit at the tens place be x.

So, the number at the unit place will be 12–x.

So, the two digit number is 10x+(12–x)=9x+12

The number obtained by reversing the digits=10×(12–x)+x=120–9x

According to the condition,

(9x+12)÷(120–9x)=7÷4

So, 4(9x+12)=7(120–9x)

Therefore, 36x+48=840–63x

Thus, 99x=792, so x=8

The digit at units place=12–x=4

Thus, the number is 84.

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The tens digit of a two-digit number exceeds the units digit by 2. If the number is increased by ninth and then divided by the sum of the digits, the quotient is 7. What is the number?

Let the number be ab where a is the tens digit and b is the units digit

The number can be expressed as 10a + b

We are told a = b+2

The number can be written as 10( b+2) + b = 11b + 20

Increasing it by 9 ( increasing by a ninth doesn’t give whole number values for a and b) we get 11b + 29

We are told that dividing this by the sum of digits a and b gives quotient 7

So, (11b + 29)/( 2b+2) = 7

11b + 29 = 14b + 14 15 = 3b

So b=5 and a = 5+2=7

The number is 75 Hélio Waldman

Retired Professor, Collaborating Professor at University of Campinas (UNICAMP) (1973–present)Author has 464 answers and 285.9K answer views3y

Let “ab” be the decimal representation of the given number. Then:

(10a+b)/(10b+a) = 7/4

So: 40a+4b = 70b+7a

Therefore: 33a = 66b, so a = 2b

On the other hand: a+b = 12 = 3b, so b=4 and a=8

In conclusion, the number is 84.

Satyanarayana Mudunuri

Worked at ITC Limited (1979–2002)Author has 2.9K answers and 1M answer views3y

If 10x+y is the number, we have (10x+y)/(10y+x)= 7/4 and x+y=12

70y+7x = 40y+4y => 66y=33x => 2y=x, x+y=3y=12 or y=4, x=8

The number is 84 Sponsored by USAFIS

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From all three digit numbers, what is the one that when divided by the sum of digits gives the largest result?

Well this question can be said as the mother question of a number of questions. If we observe quite carefully…we can say that there exists a general trend of the value of(number/sum of its digits) for three digit numbers!

Here is a graph which represents this. y- axis value of m

where m= number/sum of digits

i.e m= ( 100x+10y+z)/(x+y+z) 100x+10y+z)/(x+y+z)

x-axis =a three digit number_xyz_

_xyz_

with increasing numerical value

x,y,z belongs to integers from 0 to 9, x not equals to 0

Now, let me provide the salient features of this graph

peaks.

The peaks of the graph represents the numbers in the format _x00_

_x00_ all have the same Ashis Ghosh

Former Retired officer at State Bank of India (SBI)Author has 2.2K answers and 2.1M answer views3y

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Mohammed 1 month ago

Guys, does anyone know the answer?