Sum of the digits of a three digit number is 7 and the digit at ten’s place is unity. On
reversing the order of the digits, the new number obtained is 16 less than twice the
original number. Find the number.

Question

Sum of the digits of a three digit number is 7 and the digit at
ten’s place is unity On
reversing the order of the digits, the new number obtained is 16
less than twice the
original number Find the number

Shruti Tyagi · Accepted Answer

Dear Student,

Let the 3 digit number be xyzsince the 10's digit is unity hence y=1Also the sum of 3 digits =7i
e x+1+z=7⇒x+z=6  --1Hence the number is x1z=100x+10+zon reversing the digit we get z1x=100z+10+xNow the new number obtained is 16 less than twice the originalHence 100z+10+x=2×100x+10+z-16⇒100z+10+x=200x+20+2z-16⇒100z+10+x=200x+4+2z⇒199x-98z-6=0  --2taking values from equation 1z=6-x⇒199x-986-x-6=0⇒199x-588+98x-6=0⇒297x-594=0⇒297x=594⇒x=2putting value in equation 1 we get x+z=6⇒z=6-2⇒z=4Hence the number is 214
Regards,

Sum of the digits of a three digit number is 7 and the digit at ten’s place is unity. On reversing the order of the digits, the new number obtained is 16 less than twice the original number. Find the number.

Sum of the digits of a three digit number is 7 and the digit at ten’s place is unity. On
reversing the order of the digits, the new number obtained is 16 less than twice the
original number. Find the number.