5
09. A ship left caleulla port on December 3 in
the year 1989 and referoned on
march
1960 for how many days was the slip away
from the boot
co
Ioanne
Answers
Answer:
5
09. A ship left caleulla port on December 3 in
the year 1989 and referoned on
march
1960 for how many days was the slip away
from the boot
co
Ioanne
Step-by-step explanation:
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10th
Maths
Pair of Linear Equations in Two Variables
Algebraic Solution of a Pair of Linear Equations
Form the pair of linear equ...
MATHS
Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method :
(i) A part of monthly hostel charges is fixed and the 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 charges and the cost of food per day.
(ii) A fraction becomes
3
1
when 1 is subtracted from the numerator and it becomes
4
1
when 8 is added to its denominator. Find the fraction.
(iii) 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?
(iv) Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
(v) The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.
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ANSWER
i) Let the fixed monthly hostel charges be Rs. x and the cost of food per day taken from the mess be y.
As per the given condition,
x+20y=1000 ...(1)
x+26y=1180 ...(2)
Subtracting eq(1) from eq (2), we get
⇒6y=180
⇒y=30
Substitute y=30 in eq (1), we get
⇒x+20(30)=1000
⇒x+600=1000
⇒x=400
So, the fixed monthly hostel charge is Rs. 600 and the cost of food per day is Rs. 30.
ii) Let the numerator be x and the denominator be y, so the fraction will be
y
x
.
y
x−1
=
3
1
⇒3x−y=3⇒3x−3=y ...(1)
y+8
x
=
4
1
⇒4x=y+8 ...(2)
Substituting for y in (2) we get,
4x=3x−3+8
x=5
putting x=5 in eq(1) we get y=12
∴fraction=
y
x
=
12
5
iii) Let x be the number of correct answers and y be the number of wrong answers.
So, 3x−y=40 ...(1)
4x−2y=50 ...(2)
Multiplying (1) by 2, we get
6x−2y=80 ...(3)
4x−2y=50 ...(4)
Subtracting eq(4) from eq(3), we get
⇒2x=30
⇒x=15
Putting x=15 in eq (1), we get
⇒3(15)−y=40
⇒y=5
So, Correct answers =15 and wrong answers =5.
Total number of questions in the test =x+y=20.
iv) Let the speeds of the first and second cars be x km/hr and y km/hr
respectively.
Distance between places A and B =100km.
Moving in the same direction, relative speed will be =x−y
5×(x−y)=100
⇒x−y=20 ...(1)
Moving in opposite directions, relative speed will be =x+y
⇒1×(x+y)=100⇒x+y=100 ...(2)
Adding (1) and (2), we get
⇒2x=120
⇒x=60
Substitute in eq (1), we get
⇒y=40
The speeds of the first and second cars are 60 km/hr and 40 km/hr respectively.
v) Let the length of rectangle be l and the breadth be b.
So, the area will be A=l×b.
Case 1:
l
′
=l−5
b
′
=b+3
A
′
=A−9=lb−9
⇒(l−5)(b+3)=lb−9
⇒lb+3l−5b−15=lb−9
⇒3l−5b=6....(1)
Case 2:
l
′′
=l+3
b
′′
=b+2
A
′′
=A+67=lb+67
(l+3)(b+2)=lb+67
⇒lb+2l+3b+6=lb+67
⇒2l+3b=61...(2)
Multiplying (1) by 3 and (2) by 5 and adding both equations, we get
9l−15b=18 ...(3)
10l+15b=305 ...(4)
Adding eq (3) and eq (4), we get
19l=323
⇒l=17
Putting l=17 in eq(1), we get
⇒3(17)−5b=6
⇒45=5b
⇒b=9
The length and breadth of the rectangle are 17 and 9 units respectively