15. A man is 4 times as old as his son. After 16 years he will be only twice as old as his son.
Find their present ages.
16. A man is thrice as old as his son. Five years ago the man was four times as old as his son.
Find their present ages.
17. After 16 years, Fatima will be three times as old as she is now. Find her present age.
18. After 32 years, Rahim will be 5 times as old as he was 8 years ago. How old is Rahim today?
19. A bag contains 25-paisa and 50-paisa coins whose total value is 30. If the number of
25-paisa coins is four times that of 50-paisa coins, find the number of each type of coins.
20. Five times the price of a pen is 17 more than three times its price. Find the price of
the pen.
21. The number of boys in a school is 334 more than the number of girls. If the total strength of
the school is 572, find the number of girls in the school.
22. The length of a rectangular park is thrice its breadth. If the perimeter of the park is 168
metres, find its dimensions.
23. The length of a rectangular hall is 5 metres more than its breadth. If the perimeter of the
hall is 74 metres, find its length and breadth.
24. A wire of length 86 cm is bent in the form of a rectangle such that its length is 7 cm more
than its breadth. Find the length and the breadth of the rectangle so formed.
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Answers
Answer:
(15) Let Son's age =x and Man's age =4x
After 16 years,
2(x+16)=4x+16
2x+32=4x+16
16=2x
x=8 years
∴ Son's age =8 years and Man's age =32 years.
(16)
Let the present ages of the man and his son be "x " and "y" respectively.
As per the question,
x=3y -------> (1)
Ages five years ago,
age of father = x−5
age of son =y−5
So,
x−5=4(y−5)
x−5=4y−20
from equation (1)
3y−5=4y−20
4y−3y=−5+20
y=15
x=3y
x=3∗15=45
Hence, present ages of father and son are :-
age of father = x=45years
age of son = y=15years
(17)
Let Fatima's current age be x
Then 16 years from now her age is=x+16
According to question
x+16=3x
⇒16=3x−x
⇒16=2x
⇒
2
16
=x
∴x=8
Therefore Fatima's current age is 8 years
(18)Rahim is 18 years old today. Thus, the present age of Rahim is 18 yrs.
(19)Total amount in the bag = Rs. 30=3000 paise
Let the number of 50 paise coins be x
Then the number of 25 paise coins =4x
Now, according to the question
25(4x)+50x=3000
100x+50x=3000
150x=3000
x=
150
3000
x=20
4x=80
Therefore, number of 50 paise coins =20
Number of 25 paise coins =80
(20)
Let the price of the pen be x
⇒5x=3x+17
⇒5x−3x=17
⇒2x=17
⇒x=
2
17
⇒x=8.5
∴ the price of the pen is 8.5 rupees
(21)
Let the number of girls be x
Number of boys =x+334
total strength =572
⇒x+x+334=572
⇒2x+334=572
⇒2x=238
⇒x=
2
238
=119 girls
(22)Let length=x
Then, x=3Breadth
⇒B=
3
x
Area=x⋅
3
x
Perimeter=2(x+
3
x
)=168m.
2×
3
4x
=168
⇒x=
8
3×168
x=63m.
Length=126m
Breadth=
3
63
=21m.
(23)Given: Length of the rectangular hall=5+breadth of the rectangular hall
⇒l=5+b
Perimeter of the rectangular hall=2(l+b)
⇒74=2(5+b+b)
⇒5+2b=
2
74
=37
⇒2b=37−5=32m
∴b=
2
32
=16m
∴l=5+b=5+16=21m
∴length=21 m and breadth=16 m
(24)ANSWER
Let the length of rectangle=l
⇒ breadth=l−7
⇒ Perimeter of rectangle=2(l+b)= Length of wire
⇒2(l+l−7)=86
⇒2l−7=43
⇒2l=50
⇒l=25cm
⇒ Breadth=18cm.
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