Q.1 After 12 years Kanwar shall be 3 times as old as he was 4 years ago. find his present age?
Q.2 The sum of the digits of a two-digit number is 8. When the digits are reversed the number increases by 18 what is the original number?
Q.3 Carpenter charged Rs. 2500 for making a bed. The cost of materials used is Rs. 1100 and the and the labour charges Rs. 200/hr. Did how many hours did the carpenter work?
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Answers
SOLUTION
1) Let Kanwar's present age be 'x'
=) His age before 4 years= x-4
=) His age after 12 years= x+12
Since age after 12 years = 3times age before 4 years
=) x+12= 3(x-4)
=)x+12= 3x-12
=) 3x-x= 12+12
=) 2x= 24
=) x= 24/2
=) x= 12 {present age is 12 years} ans.
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2) Let the Two digit no.be xy
=) x+y= 8
=) Now algebraically;
=) x+y= 8---------{eq^n 1}
=) The value of xy is 10x+y
=) The value of yx is 10y+x
=) 10y+x= 10x+y+18
=) 9y-9x=18
=) 9(y-x)=18
=) y-x,= 2
From eq^n 1
y= 8-x
=) 8-x-x=2
=) 8-2x=2
=) -2x= -6
=) x= 3
so,
=) y-x=2
=) y-3=2
=) y= 2+3
=) y= 5
Therefore, original no. xy= 35 ans.
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3)Cost of material = Rs.1100
=) Total amount given to carpenter= Rs. 2500
=) amount given for labour = (2500-1100)Rs. = 1400Rs.
=) Charges labour per hour= 200Rs.
=) Number of hours labour worked = 1400/200= 7 hours. [Answer]
HOPE IT HELPS
Answer:
Let the two digit number be xy
x + y = 8
Right away I can logically see that, since the value
increases if the digits are reversed, our choices are:
17
26
35
If I reverse 17 I get 71 .. This is more than an 18 increase
If I reverse 26 I get 62 ... This is more than an 18 increase
If I reverse 35 I get 53... 35 + 18 = 53 so this is my answer
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Now algebraically:
x + y = 8 {equation 1}
The value of xy is 10x + y
The value of yx is 10y + x
10y + x = 10x + y + 18
9y - 9x = 18
9(y - x) = 18
y - x = 2
From equation 1: y = 8-x
8 - x - x = 2
8 - 2x = 2
-2x = -6
x = 3
y - x = 2
y - 3 = 2
y = 5
Original number xy = 35
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