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Pair of Linear Equations Practice 3: Word Problems and Modelling

Section A: Model the Situation

Question 1mcq
The sum of two numbers is 4040 and their difference is 88. If the numbers are xx and yy with x>yx>y, which equations model this?
A.x+y=40x+y=40, x−y=8x-y=8
B.x−y=40x-y=40, x+y=8x+y=8
C.xy=40xy=40, x−y=8x-y=8
D.x+y=8x+y=8, xy=40xy=40
Question 2mcq
A ticket counter sold adult tickets at ₹80₹80 and student tickets at ₹50₹50. Total tickets sold were 3030 and total money collected was ₹2100₹2100. If adult tickets are aa and student tickets are ss, which pair is correct?
A.a+s=30a+s=30, 80a+50s=210080a+50s=2100
B.80a+50s=3080a+50s=30, a+s=2100a+s=2100
C.a+s=2100a+s=2100, 80a+50s=3080a+50s=30
D.80s+50a=210080s+50a=2100, a−s=30a-s=30
Question 3mcq
A fruit seller sold 22 kg apples and 33 kg oranges for ₹360₹360. Another customer bought 44 kg apples and 11 kg oranges for ₹440₹440. If apple price is aa and orange price is oo per kg, what is aa?
A.9090
B.8080
C.7070
D.100100
Question 4mcq
Two pens and three notebooks cost ₹160₹160. Four pens and one notebook cost ₹140₹140. What is the cost of one notebook?
A.3636
B.2828
C.4040
D.2424
Question 5mcq
A student defines xx as the present age of Riya and writes x+5x+5 for Riya’s age 55 years ago. What is the error?
A.It should be x−5x-5, not x+5x+5
B.It should be 5x5x
C.It should be x/5x/5
D.There is no error

Section B: Apply and Analyse

Question 6mcq
A problem says: “A rectangle has perimeter 5050 cm.” A student writes l+b=50l+b=50. What is the modelling mistake?
A.The correct equation is 2(l+b)=502(l+b)=50
B.The correct equation is lb=50lb=50
C.The correct equation is l−b=50l-b=50
D.No mistake; perimeter equals l+bl+b
Question 7mcq
A two-digit number has digit sum 1111. Reversing the digits gives a number 2727 more than the original. If tens digit is xx and ones digit is yy, which pair models it?
A.x+y=11x+y=11, 10y+x=10x+y+2710y+x=10x+y+27
B.x+y=27x+y=27, 10x+y=1110x+y=11
C.10x+y=1110x+y=11, x−y=27x-y=27
D.x+y=11x+y=11, 10x+y=10y+x+2710x+y=10y+x+27
Question 8mcq
The sum of the digits of a two-digit number is 99. Reversing the digits gives 2727 less than the original. What is the original number?
A.6363
B.7272
C.5454
D.8181
Question 9mcq
Which substitution correctly checks whether (5,2)(5,2) satisfies 3x+4y=233x+4y=23?
A.3(5)+4(2)=233(5)+4(2)=23
B.3(2)+4(5)=233(2)+4(5)=23
C.3+5+4+2=233+5+4+2=23
D.5+2=235+2=23
Question 10mcq
Assertion: The pair 2x+3y=72x+3y=7 and 4x+6y=144x+6y=14 has infinitely many solutions. Reason: The ratios a1/a2a_1/a_2, b1/b2b_1/b_2 and c1/c2c_1/c_2 are equal. Choose the correct option.
A.Both assertion and reason are true, and the reason explains the assertion.
B.Both are true, but the reason does not explain the assertion.
C.Assertion is true, but reason is false.
D.Assertion is false, but reason is true.