Exercise 4A
Question 1
The sum of the digits of a 2-digit number is 12. The number is 6 times the units digit. Find the number.
Sol :
2 digit number=10a+b
a+b=12⇒b=12-a
b×6=10a+b
6b=10a+b
10a+(12-a)=6(12-a)
10a+12-a=72-6a
9a+6a=72-12=60
15a=60
$a=\frac{460}{15}=4$
b=12-4=8
The number=10a+b
=(10×4)+8=48
Question 2
The sum of the digits of a 2 digit number is 7. If the digits are reversed, the new number increased by 3 equals 4 times the original number. Find the original number.
Sol :
The original number=10a+b
a+b=7⇒b=7-a...(i)
Reversed number=10b+a
according to question
4(10a+b)-(10b+a)=3
40a+b-10b-a=3
40a-a+b-10b=3
39a-6b=3
39a-6(7-a)=3 [From (i)]
39a-42+6a=3
39a+6a=3+42
45a=45
a=1
∴b=7-1=6
∴original number=10a+b=10×1+6
=16
Question 3
The sum of a number of two digits and of the number formed by reversing the digits is 110 and the difference of the digits is 6. Find the number.
Sol :
b-a=6⇒b=6+a
Original number=10a+b
Reversed number=10b+a
(10a+b)+(10b+a)=110
10a+b+10b+a=110
11a+11b=110
a+b=10
a+6+a=10
a=2
∴b=6+2=8
∴original number=10a+b=10×2+8
=28
Question 4
A certain number between 10 and 100 is 8 times the sum of its digits. If 45 is subtracted from it the digits will be reversed. Find the number.
Sol :
The number between 10 and 100
The number will be 2 digit number=10a+b
According to the question
(10a+b)=8(a+b)
10a+b=8a+8b
10a-8a=8b-8b
2a=7b
2a-7b=0
According to question
(10a+b)-45=10b+a
10a+b-(10b+a)=45
10a+b-10b-a=45
9a-9b=45
a-b=5
a=5+b
Now, 20-7b=0
2(5+b)-7b=0
10+2b-7b=0
-5b=-10
b=2
∴a=5+b=5+2=7
∴The number=10×7+2=72
Question 5
A number consists of three digits, the right hand being zero. if the left hand and the middle digits are interchanged the number is diminished by 180. If the left hand digit is halved and the middle and right hand digits are interchanged the number is diminished by 454. Find the number.
Sol :
Original number=100a+10b+0
=100a+10b
According to the question
(100a+10b)-(100b+10a)=180
100a+10b-100b-10a=180
90a-90b=180
a-b=2
According to question
$100\times \frac{a}{2}+0+b=50a+b$
(10a+10b)-(50a+b)=454
50a+9b=454
50(2+b)+9b=454
100+50b+90=454
59b=454-100
59b=354
$b=\frac{354}{59}$
b=6
∴a=2+b=2+6=8
The number=100a+10b+0
=(100×8)+10×6+0
=800+60
=860
Hmmm.. there is a mistake you should solve it in question number 2.
ReplyDeleteI was also confused that why it is 6b
BTW thanks for the solution and thanks for helping me for my preparation
thanks for letting us know . we fixed it :) keep using .
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