Seven times a given two digit number is equal to four times the number obtained by inter changing th

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02 Aug 2013 Problem

Seven times a given two digit number is equal to four times the number obtained by inter changing the digits and the difference of the digits is 3. Find the numbers.

OPtion

1) 63
2) 41
3) 74
4) 36
5) 52
6) 69
7) 76
8) 96
9) 12
10) None Of these

Solution

Suppose x is digit in ten's place and y is the digit in unit's place.
So the number 10x+y
By reversing the order of the digits, the new Number is 10y+x
According to the given condition 7(10x+y)=4(10y+x)
Also x-y=3
Solve
number is 36
option 4

Correct Option: 4 Best Solution (27)

Balakrishnan M   11 years AGO

Seven times a given two digit number is equal to four times the number obtained by inter changing the digits
7(10x+y)=4(x+10y)
70x+7y=4x+40y
66x-33y=0
2x-y=0
2x=y
The difference of the digits is 3
y-x=3
2x-x=3
x=3
y=6
that number is 36.

Like? Yes (194) | No (46)  

NITISH KUMAR   11 years AGO

7(10y+x)=4(10x+y);
x-2y=0......(1)
x-y=+/-3......(2)
from 1 and 2
y=3ory=-3
y=3 is possible
so number is 10(3)+6=36
36 is the number

Like? Yes (61) | No (30)  

krishnapriya   11 years AGO

Let the unit digit and 10's digit be x an y respectively. So, the number is 10y+x and when the number is reversed, then the number is 10x+y.
Also,x-y=3-------(1) and
7(10y+x)=4(10x+y)
70y+7x=40x+4y
2y-x=0-------(2)
adding (1) and (2) we have,
y=3 and x=6
hence the number is 10y+x=10x3+6=30+6=36

Like? Yes (42) | No (23)  

sandeep pandey   11 years AGO

let the no be 10x+y
7 times is 70x+7y
no obtained by interchanging the digit is 10y+x
4 times is 40y+4x
therefore,
70x+7y=40y+4x
=>66x=33y
=>2x-y=0.......(1)
we know
either x-y=3 or y-x=3.(2)
solving we get x=-3,3
x=3 y=6
therefore no is 36

Like? Yes (27) | No (13)  

Pankaj   11 years AGO

by the given conditions 2 eqs. r formed:
7(10x+y)=4(10y+x)____________(1)
y-x=3________________(2)
x being no. at tens place
y being no. at ones place
(1) equ. becomes: 2x-y=0
putting the value of y=x+3 in above v get
2x-x-3=0
=> x=3 and y=6(by solving from above equation)

Like? Yes (24) | No (18)  

Chandni Maurya   11 years AGO

ans=36
let two digits are a&b,
=> 7*(a*10+b)=4*(b*10+a)
=> 70a + 7b = 40b + 4a
=> 66a - 33b =0
=> 2a - b =0 ---(1).
according to ques, |a-b|=3
from eq. (1). we can conclude=> b-a=3
=> b=a+3
put it in (1)
2a-a-3=0
=> a=3, =>b=a+3=3+3=6
so no. is= 36

Like? Yes (20) | No (14)  

Vinay Sipani    11 years AGO

7(10x + y) = 4(10y + x)
=> 2x = y

Also (y - x) = 3

=> x = 3 , y = 6

Like? Yes (28) | No (23)  

jitendra sharma   11 years AGO

suppose two digit no is ab,
by interchanging digits ab becomes ba;
given 7ab=4ba;
ab/ba=4/7;difference bw digit=3;
so the ans=36

Like? Yes (26) | No (22)  

Tirtha Bhattacharya   11 years AGO

Let tha digit in units\'s place be x and in ten\'s place be y
then the number is 10y+x
By the problem,
7(10y+x)=4(10x+y)
or,33x-66y=0
or,x-2y=0...........(1)
Again,x-y=3.........(2)
solving (1)and (2),
x=6 and y=3
so the number is 36

Like? Yes (17) | No (13)  

Priyanka Sharma   11 years AGO

Let the digits of the no. be x and y.
Then no. is 10x+y.
Given that 7(10x+y)=4(10y+x)
Simplify it to get y=2x
Another condition given is |x-y|=3
Using both equations, we get x=3 and y=6.
Therefore the no. is 36.

Like? Yes (11) | No (7)  

nithya   11 years AGO

ans: 36.
from option,
7(36) = 252; 4(63) =252
7(36)=4(63) =252. And difference between two digits is 3.It satisfies the given condition.

Like? Yes (14) | No (11)  

Anilkumar   11 years AGO

7(10x+y)=4(10y+x)
Solving we get 2x=y
Applying second condition answer is 36

Like? Yes (14) | No (12)  

kiruthika   11 years AGO

the answer is 36
36*7=252
by reversing the digits we get
63*4=252
then
the diff between the digits is 6-3=3
so the number is 36

Like? Yes (11) | No (10)  

SATYAM SAURABH   11 years AGO

better eliminate option than the solve whole problem
from the last condition only 1, 2, 3, 4,6,8. n use condition 1 you will your answer

Like? Yes (10) | No (9)  

Anil Kumar Bharti   11 years AGO

Exp: Using options
36*7=63*4

Like? Yes (9) | No (9)  

FRANKLIN VIJAY   11 years AGO

36*7=252
63*4=252
6-3=6
So answer is 36

Like? Yes (7) | No (7)  

rajkumar m   11 years AGO

36*7=252 63*4=252 6-3=3

Like? Yes (9) | No (9)  

Amrit Anand   11 years AGO

let the 2 digit number =10*x+y & another will be 10y+x A/c to question
go through option
7*36=4*36
* diff between digit=3
so ans:-36

Like? Yes (7) | No (7)  

Deepak Sharma   11 years AGO

Let tens digit of number is x and unit digit is y.
then the two digit number is 10x-y.
therefore by first condition,
7(10x+y)=4(10y+x)
2x-y=0..................equation 1
from second condition
x-y=3.................equation 2
by solving equation 1 & 2, we get
x=3, y=6
then that two digit no. is 36
so option 4 is correct.

Like? Yes (11) | No (11)  

gulshan kumar   11 years AGO

Y =2 x & x -y =3
By solving these two equations, we get the 36

Like? Yes (1) | No (1)  

Sachin Singh Gusain   11 years AGO

using the equations
7(10X+Y)=4(10Y+X) and Y-X = 3
we get X=3 and Y=6

Like? Yes (8) | No (8)  

mandira kundu   11 years AGO

check all d options given.
if original/interchanged=4/7 then that will b d ans.
ans-36

Like? Yes (8) | No (8)  

mohamed ismail   11 years AGO

7*36=252
4*63=252
and also it satisfies the second condition too
6-3=3.

Like? Yes (7) | No (8)  

Gaurav Sharma   11 years AGO

let us take the 4 option which is 36
36*7=252
reverse of digits is 63
63*4=252
so is the answer

Like? Yes (8) | No (9)  

sajjan kumar   11 years AGO

opposite of number should be divisible by 7.
36*7=4*63

Like? Yes (10) | No (11)  

Udhaya kumar   11 years AGO

fro given data
7(10x+y) = 4(10y+x)
then y-x=3 (because y is greater than x)
by solving this we get x=3 and y=6
so answer is 36.............

Like? Yes (12) | No (14)  

ABHISHEK KUMAR MISHRA   11 years AGO

let x is on unit place and y is on ten's place so the no is: 10y + x
when reverse the digit then no is: 10x + y
now according to question
7(10y + x)= 4(10x + y)......(1)
and difference is:
x - y = 3.....(2)
now solve (1) & (2) then
x=6 & y=3
so the no is 36

Like? Yes (10) | No (12)