SOLVING WORD PROBLEMS USING CROSS MULTIPLICATION METHOD

Problem 1 :

A part of monthly hostel charges is fixed and remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs.1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs.1180 as hostel charges. Find the fixed charge and the cost of food per day.

Solution :

Let “x” be the fixed charge

Let “y” be the charge of food per day

x + 20y  =  1000

x + 26y  =  1180

x + 20y – 1000  =  0  ------(1)

x + 26y – 1180  =  0   ------(2)

x/(-23600 + 26000)  =  y/(-1000 + 1180)  =  1/(26 - 20)

x/2400  =  y/180  =  1/6

x/2400  =  1/6           y/180  =  1/6

x  =  2400/6                y  =  180/6

x  =  400                      y  =  30

Therefore the fixed charge  =  Rs.400

Charge of food per day  =  Rs.30

Problem 2 :

A fraction becomes 1/3 when 1 is subtracted from the numerator it becomes 1/4 when 8 is added to its denominator. Find the fraction.

Solution :

Let “x/y” be the required fraction

(x – 1)/ y  =  1/3

3(x – 1)  =  1 y

3x – 3  =  y

3x – y – 3  =  0 ----------(1)

x/(y + 8)  =  1/4

4x  =  1(y + 8)

4x  =  y + 8

4x – y – 8  =  0  ----------(2)

x/(8 – 3)  =  y/(-12 + 24)  =  1/(-3 + 4)

x/5  =  y/12  =  1/1

x/5  =  1         y/12  =  1

x  =  5               y  =  12

So, the required fraction is 5/12

Problem 3 :

Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?

Solution :

Let “x” be the number of questions answered correctly

Let “y” be the number of questions answered incorrectly

3x  – 1y  =  40

4x – 2y  =  50

3x – 1y – 40  =  0  ---------(1)

4x – 2y – 50  =  0   ---------(2)

x/(50 – 80)  =  y/(-160 + 150)  =  1/(-6 + 4)

x/(-30)  =  y/10  =  1/(-2)

x  =  -30/(-2)         y  =  10/(-2)

x  =  15                  y  =  5

So, the number of questions answered correctly = 15

Number of questions answered incorrectly = 5 

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