M4maths Previous Puzzles

05 Jul 2013 Three digit

Sum of 3 digit of a three digit number is 17. On reversing the digits, the difference of new number & previous number is 297. If units place digit is 3 less then the sum of other two digits. Then product of the digits of the number is..

OPtion

1) 18
2) 63
3) 64
4) 72
5) 144
6) 162
7) 168
8) 180
9) 189
10) None of these

Solution

Let digits are x, y, (17-x-y)
number [100x+10y+(17-x-y)]
By the given condition
[100(17-x-y)+10y+x]-[100x+10y+(17-x-y)]=297
100(17-2x-y)-(17-2x-y)=297
99(17-2x-y)=297
17-2x-y=3
2x+y=14 (i)
17-x-y=x+y-3
2x+2y=20
x+y=10
4
6
7
option 7

Correct Option: 7 Best Solution (7)

Sagar Jinachandran   11 years AGO

let x,y,z be the hundredths place, tens place, and unit's place respectively
then
x+y+z=17------(1)
100z+10y+x-(100x+10y+z)=297
99z-99x=297
or -x+z=3-----(2)
z=x+y-3
x+y-z=3---(3)
solving 1 & 3
we get x+y=10----(4)
putting 4 in 3 we get
10-z=3
z=10-3=7
putting z value in 2 we get
-x+7=3
x=4
putting x value in 4 we get
4+y=10
y=6
so the number is 467
multiplying the digits we get 4*6*7=168
option 7

Like? Yes (15) | No (2)  

rizwanur rahman   11 years AGO

the sum of the digits are = 17 suppose the digits are x,y and z. also given that unit's digit is 3 less than sum of other two. so lets take z as the unit's digit. so x+y+(x+y-3)=17 i.e. x+y=10 the possible combinations are (1,9)(2,8)(3,7)(4,6)(5,5). the value of z=7 as z= 10-3 . out of the possible combinations 467 satisfies the given condition. so product of digits = 4.6.7=168

Like? Yes (7) | No (2)  

Roopam Jain   11 years AGO

let the no. be xyz
Solve the three equations:
x+y+z = 17
(100z+10y+x)-(100x+10y+z)=297
z=x+y-3

On solving, x=4, y=6, z=7
Hence product = 4*6*7 = 168

Like? Yes (5) | No (1)  

Himanshu Kumar Gupta   11 years AGO

Let xyz be the 3 digit no.
X+y+z=17,
Zyx-xyz=297,
Z=x+y-3
From above equations we get
X+y=10 and z=7
Now zyx-xyz will give 7 at unit place only when x=4 so y=6 therefore product is 168

Like? Yes (5) | No (1)  

Preetha Maniyalath   11 years AGO

numbers is 467
multiplying the digits we get 168
option 7

Like? Yes (4) | No (4)  

Anil Kumar Bharti   11 years AGO

Exp:
sum of digit is 17
Unit place is 3 less then sum of two digits.
so sum of 2 digit is 10 and unit digit is 7
4+6+7=17
no is 467
rev no is 764
Diff b/w them 764-462=297
So, Product of Number is 4*6*7=168

Like? Yes (3) | No (3)  

N.Dhanalakshmi   11 years AGO

sum of 3 digits x+y+z=17=>x+y=17-z
reversing the digit (zyx)
difference of new num & previous num is 297 so
(zyx)-(xyz)=297
unit place digit is less then sum of other 2 digits (x+y)-3=z; (x+y)=z+3; 17-z=z+3;z=7.
now apply this z value in x+y+z=17 so x+y=10
{(1+9),(2+8),(3+7),(4+6),(5+5)}=10
these two digit products are 9,16,21,24,25 with z value 7 so product of digits of num are 63,112,147,168,175. options given below are 63,168.
(zyx)-(xyz)=(764-467)=297.
so ans is 168.

Like? Yes (3) | No (3)