(ii) A fraction becomes when l is subtracted from the numerator and it becomes a
when 8 is added to its denominator. Find the fraction.
(un) Yash scored 40 marks in a test, getting 3 marks for each right answer and losing
mark for each wrong answer. Had 4 marks been awarded for each correct ans
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 Aland 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?
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
Answers
Answer:
Step-by-step explanation:
(ii) Let the fraction be
x
y
According to the given information,
x−1
y
=
1
3
⇒3x−y=3…(1)
x
y+8
=
1
4
⇒4x−y=8…..(2)
Subtracting equation (1) from equation (2), we obtain
x=5…(3)
Putting this value in equation (1), we obtain
15−y=3 y=12
Hence, the fractlon is
5
12 ...........
(iii) Let the number of right answers and wrong answers be x and y
According to the given information,
3
x
−
y
=
40
…
.
.
(
1
)
4
x
−
2
y
=
50
⇒
2
x
−
y
=
25
…
.
(
2
)
Subtracting equation (2) frorn equation (1), we obtain
x
=
15
…
.
(
3
)
Substituting this in equation (2), we obtain
30-y = 25
Y = 5
Therefore, number of right answers = 15
And number of wrong answers = 5
Total number of questions = 20 .................
(iv) Let the speed of
1
st
car and
2
nd
car be
u
km/h and
v
k
m
/
h
Respective speed of both cars While they are travelling in same direction = (u - v) km/h
Respective speed of both cars while they are travelling in opposite directions i.e.,
travelling towards each other = ( u +v) km/h
According to the given information,
5
(
u
−
v
)
=
100
⇒
u
−
v
=
20
…
(
1
)
1
(
u
+
v
)
=
100
…
(
2
)
Adding both the equations, we obtain
2
u
=
120
u
=
60
k
m
/
h
(3)
Substituting this value in equation (2), we obtain
v = 40 km/h
Hence, speed of one car = 60 km/h and speed of other car = 40 km/h ......
(v) Let length and breadth of rectangle be x unit and y unit respectively.
Area = xy
According to the question,
(
x
−
5
)
(
y
+
3
)
=
x
y
−
9
⇒
3
x
−
5
y
−
6
=
0
…
.
(
1
)
(
x
+
3
)
(
y
+
2
)
=
x
y
+
67
⇒
2
x
+
3
y
−
61
=
0
…
.
(
2
)
By cross multiplication method, we obtain
x
305
−
(
−
18
)
=
y
−
12
−
(
−
183
)
=
1
9
−
(
−
10
)
x
323
=
y
171
=
1
19
x
=
17
,
y
=
9
Hence, the length and breadth of the rectangle are 17 units and g units respectively. ...............