İTÜ GELİŞTİRME VAKFI
ÖZEL EKREM ELGİNKAN LİSESİ
SEMESTER HOMEWORK
Term
1st
NameSurname
Lesson
Unit
Mathematics Equations and
Inequalities
Subject
Date
Ratio and ProportionProblems
Class:
Number:
1. The distance between two cities, A and B, is 420 km and a car travels some part of this
way at 60 km/h and travels the rest of the distance at 75 km/h. If the entire trip take 6
hours, how many km does it travel at 60 km/h?
2. A train with the length of 80 m travels at 72 km/h. There are two tunnels with the
lengths of 120 m and 260 m and there is 400 m between the tunnels. In how many
seconds does the train travel from the beginning of the first tunnel to the end of the
second one?
3. Two cars 10 km apart travel in the same direction at 75 km/h and at 60 km/h. In how
many minutes the faster car overtake the slower one?
Sayfa 1 / 4
4. Anıl can do a job in 12 hours and Kaan can do it 10 hours. What part of the job can be
done in 4 hours by working together?
5. Barış can do a job in 18 days and Can do it in 24 days. How many days would it take Can
to do the rest of the job if Barış and Can did in 6 days?
6. How many kilograms of salt must be added to 60 kg of a 30% salt to produce a 40% salt?
7. How many liters of 60% solution must be mixed with 90 liters of a 90% solution to get an
80% solution?
Sayfa 2 / 4
8. Mother divided the money among İlke, Elif and Ece in the ratio 2 : 3 : 5. If Ece got 150₺,
find the total amount and the money received by İlke and Elif.
9. The perimeter of a rectangle is equal to 280 meters. The ratio of its length to its width is
5:2. Find the area of the rectangle.
10. If
a c
 a + 4b   c + 5d 
= = 4 , then find the value 

.
b d
 b  d 
11. If
a −1 b + 3 c +1
and 3a + b − 2c = 7 , then find a+b.
=
=
3
2
5
Sayfa 3 / 4
12. The geometric mean of the numbers a and b is 6, the geometric mean of a and c is 8. If
the arithmetic mean of b and c is 10, find a.
13. Mert spent
1
1
of his money and
of the rest. If his remaining money is 75 ₺ , what is
4
6
his money at the beginning?
14. A mother’s age is equal to the sum of her three children’s age. 5 years later, two times of
mother’s age will be 25 more than the sum of her children’s age. What is the present age
of mother?
15. If a shirt is sold with 15% loss, its selling price is 42,50 ₺. How much would the selling
price be if it is sold with 60% profit?
Sayfa 4 / 4