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
Answer:
12 years
Step-by-step explanation:
Let x = present age
x + 12 will be my age 12 years from now.
3(x-4) will be three times as old as I was 4 years ago
x+12 = 3(x-4)
Solve for x
x+12 = 3x - 12
subtract x from both sides
12 = 2x - 12
add 12 to both sides
24 = 2x
divide both sides by 2
12 = x
The present age men is 12 years
question 2
Let us assume the digits of a number as 'x' and 'y'. Since it is a 2 digit number, we have one's place and ten's place. ( i.e., The place value of one digit is multiple of 10 and the place value of other digit is one.) I assume you know the difference between place value and face value.
Now going to the problem,
Sum of two digits is 8. => x +y=8→A
Diff between number and its reverse:
=> (10x+y)-(10y+x)=18
=>9x-9y=18
=> x-y=(18/9)=2→B
Solving A and B
x+y=8
x-y=2
=>2x=10=>x=5. Hence y = 3.
Hence the required number is 53
x+12 = 3x - 12
subtract x from both sides
12 = 2x - 12
add 12 to both sides
24 = 2x
divide both sides by 2
12 = x
The present age men is 12 years
question 3
Rs 2500 - Rs 1100 = 1400
1400/200=7
so the carpenter work for 7 hours.
first subtract carpenter charged rupees to cost of material used. Than divide the subtract answer from labour charges.
SOLUTION
1) Let Kanwar's present age be 'x'
Let Kanwar's present age be 'x'=) His age before 4 years= x-4
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.
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.
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]
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