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3 pencils and 5 pens together cost ₹101, whereas 5 pencils and 3 pens together cost ₹91. The cost of 2 pencils and 2 pens together is:
₹45
₹36
₹48
₹32
₹48
Add both linear equations to get 8x+8y=192. Divide by 4 directly to obtain the cost of 2 pencils and 2 pens (2x+2y=4192=48).
Cost of 3 pencils and 5 pens = ₹101; Cost of 5 pencils and 3 pens = ₹91
(3x+5y=101) and (5x+3y=91)
Add both linear equations to get 8x+8y=192. Divide by 4 directly to obtain the cost of 2 pencils and 2 pens (2x+2y=4192=48).
Solving for individual cost of pencils and pens (x and y) unnecessarily, which takes extra time in the exam hall.
Step 1: Set up the equations
Let the cost of one pencil be x and the cost of one pen be y. According to the problem:
3x+5y=101— (Equation 1)
Step 2: Set up the second equation
Using the second given statement:
5x+3y=91— (Equation 2)
Step 3: Add both equations
Adding Equation 1 and Equation 2 gives:
(3x+5x)+(5y+3y)=101+91⟹8x+8y=192
Step 4: Find the cost of 2 pencils and 2 pens
Divide both sides by 4 to get the combined cost of 2 pencils and 2 pens:
2x+2y=4192=48
C is correct because adding the two linear equations yields 8x+8y=192, and dividing by 4 gives 2x+2y=48.
When coefficients of variables are symmetrical (e.g. ax+by=m and bx+ay=n), always check the sum and difference of the equations first before attempting substitution or elimination.