Question

Solve the following


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Answer 1

Answer:

1

Let the present age of Kanwar is x years

Kanswar's age after 12 years = (x + 12) years

Kanwar's age 4 years ago = (x – 4) years

Given (x + 12) = 3(x – 4)

⇒ x + 12 = 3x – 12

⇒ 12 + 12 = 3x – x = 2x

⇒ 2x = 24

Hence x = 12

Kanwar's present age is 12 years.

2

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

3

Let the carpenter worked for x hr.

Given, labour charge = Rs. 200 per hr

Then, total labour charge = Rs. 200x

As, amount charged by carpenter for making a bed = cost of materials + total labour charge

∴2500 = 1100 + 200x

200x = 2500-1100

200x = 1400

Hence, the carpenter worked for 7hrs

Answer 2

Answer:

Let Kanwar's present age be x

Then,

After 12 yrs=(x+12)years

4years ago=(x-4)years

After 12 years Kanwar age is given as 3(x-4)years.

So,(x+12)=3(x-4)

x+12=3x-12

12+12=3x-x

24=2x

x=12 years.

So, Kanwar's present age is 12 years.