In this page word problem solution5 we are going to
see solution for first word problem of the worksheet cross multiplication
method.

Formulate the following problems as a pair of equations,and hence find their solutions:

(ii) In a rectangle,if the length is increased and breadth is reduced each by 2 cm then the area is reduced by 28 cm². If the length is reduced by 1 cm and the breadth is increased by 2 cm,then the area increases by 33cm². Find the area of the rectangle.

**Solution:**

Let x be the length of the rectangle

Let y be the breadth of the rectangle

Area of the rectangle = x y

length is increased and breadth is decreased by 2, so that the area is reduced by 28 cm²

(x + 2) (y -2) = x y - 28

x y - 2 x + 2 y - 4 = x y - 28

2 x - 2 y = 28 - 4

2 x - 2 y = 24

Divide the whole equation by 2 we get

x - y = 12 ----- (1)

to form the second equation we have to consider the given information from the question that is length is reduced by 1 cm and the breadth is increased by 2 cm,then the area increases by 33cm².

(x-1) (y+2) = x y + 33

x y + 2 x - y - 2 = x y + 33

2 x - y + x y - x y = 33 + 2

2 x - y = 35 ----- (2)

x - y = 12

2 x - y = 35

(-) (+) (-)

--------------

-x = -23

x = 23

Substitute x = 23 in the first equation we get

x - y = 12

23 - y = 12

- y = 12 - 23

- y= - 11

y = 11

Therefore the length of the rectangle = 23 cm

Breadth of the rectangle = 11 cm

**Verification:**

x – y = 12

23 - 11= 12

12 = 12

word problem solution5 word problem solution5

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- Elimination method
- Elimination method worksheet
- Cross Multiplication Method
- Word problems on age
- Word problems on digits
- Word problems on numbers
- Word problems on percents
- Mixed word problems

(i) One number is greater than thrice
the other number by 2. If 4times the smaller number exceeds the greater by 5,
find the numbers. Solution

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(iii) A two digit number is seven times the sum of its digits. The number formed by reversing the digits is 18 less than the given number. Find the given number. Solution

(iv) Three chairs and two tables cost $700 and five chairs and three tables cost $1100.What is the total cost of 2 chairs and 3 tables. Solution

(vi) A train traveled a certain distance at a uniform speed. If the train had been 6 km/hr faster,it would have taken 4 hours less than the scheduled time. If the train were slower by 6km/hr, then it would have taken 6 hours more than the scheduled time. Find the distance covered by the train. Solution