8. Ratio and proparation
Introduction part and excersice 5.1👇
Exercise -5.1
(1) Find the ratio of the following
(i) Smita works in office for 6 hours and Kajal works for 8 hours in her office. Find the ratio of their working hours.
(ii) One pot contains 8 litre of milk while other contains 750 milliliter.
(iii) Speed of a cycle is 15km/h and speed of the scooter is 30km/h.
(2) If the compound ratio of 5:8 and 3:7 is 45:x. Find the value of x.
(3) If the compound ratio of 7:5 and 8:x is 84:60. Find x.
(4) The compound ratio of 3:4 and the inverse ratio of 4:5 is 45:x. Find x.
(5) In a primary school there shall be 3 teachers to 60 students. If there are 400 students enrolled in the school, how many teachers should be there in the school in the same ratio?
(6) In the adjacent ΔABC, write all possible ratios by taking measures of sides pair wise.
(Hint: Ratio of AB : BC = 8 : 6)
(7) If 9 out of 24 students scored below 75% marks in a test. Find the ratio of student scored below 75% marks to the student scored 75% and above marks
(10) In triangle ABC, AB = 2.2 cm, BC = 1.5 cm and AC = 2.3 cm. In triangle XYZ, XY = 4.4 cm, YZ = 3 cm and XZ = 4.6 cm. Find the ratio AB : XY, BC : YZ, AC : XZ. Are the lengths of corresponding sides of ΔABC and ΔXYZ in proportion?
[Hint: Any two triangles are said to be in proportion, if their corresponding sides are in the same ratio]
(11) Madhuri went to a super market. The price changes are as follows. The price of rice reduced by 5% jam and fruits reduced by 8% and oil and dal increased by 10%. Help Madhuri to find the changed prices in the given table.
Item | Original price/kg | Changed Price |
Rice | ₹30 | |
| Jam | ₹00 | |
Apples | ₹280 | |
| Oil | ₹120 | |
| Dal | ₹80 |
(12) There were 2075 members enrolled in the club during last year. This year enrolment is decreased by 4%.
(a) Find the decrease in enrolment.
(b) How many members are enrolled during this year?
(13) A farmer obtained a yielding of 1720 bags of cotton last year. This year she expects her crop to be 20% more. How many bags of cotton does she expect this year?
(14) Points P and Q are both on the line segment AB and on the same side of its midpoint. P divides AB in the ratio 2 : 3, and Q divides AB in the ratio 3 : 4. If PQ = 2, then find the length of the line segment AB.
A owner increases the rent of his house by 5% at the end of each year. If currently its rent is ₹ 2500 per month, how much will be the rent after 2 years’?
Solution:
On Monday, the value of a company’s shares was ₹ 7.50. The price increased by 6% on Tuesday, decreased by 1.5% on Wednesday, and decreased by 2% on Thursday. Find the value of each share when trade opened on Friday.
Solution:
With most of the Xerox machines. you can reduce or enlarge your original by entering a percentage for the copy. Reshma wanted to enlarge a 2 cm by 4 cm drawing. She set the Xerox machine for 150% and copied her drawing. What will be the dimensions of the
copy of the drawing be’?
Solution:
The printed price of a book is ₹ 150. And discount is 15%. Find the actual amount to be paid.
Solution:
Question 6.
The marked price of an gift item is ₹ 176 and sold it for ₹ 165. Find the discount percent.
Solution:
A shop keeper purchased 200 bulbs for ₹10 each. However 5 bulbs were fused and put
them into scrap. The remaining were sold at ₹12 each. Find the gain or loss percent.
Solution:
Complete the following table with appropriate entries (Wherever possible)
Question 9.
A table was sold for ₹2,142 at a gain of 5%. At what price should it be sold to gain 10%.
Solution:
S.P. of a table = ₹ 2142
Profit = 5%
Gopi sold a watch to Ibrahim at 12% gain and Ibrahim sold it to John at a loss of 5%. If John paid ₹1,330, then find how much did Gopi sold it?
Solution:
. Let Gopi’s cost price = ₹100
Gain = 12%
∴ Gopi’s selling price to Ibrahim or Ibrahim’s cost price = ₹100 + ₹12 = ₹112
∴ Ibrahim’s loss = 5%
∴
Madhu and Kavitha purchased a new house for ₹3,20,000. Due to some economic
problems they sold the house for ₹2,80,000. Find (a) The loss incurred (b) the loss percentage.
Solution:
C.P. of a house = ₹ 3,20,000
S.P. of a house = ₹ 2,80,000
∴ C.P. > S.P.
a) Loss
= C.P. – S.P.
= 3,20,000 – 2,80,000 = 40,000
A pre-owned car show-room owner bought a second hand car for ₹ 1,50,000. He spent ₹20,000 on repairs and painting, then sold it for ₹ 2,00,000. Find whether he gets profit or loss. If so, what percent?
Solution:
Lalitha took a parcel from a hotel to celebrate her birthday with her friends. It was billed with ₹ 1,450 including 5% VAT. Lalitha asked for some discount, the hotel owner gave 8% discount on the bill amount. Now find the actual amount that lalitha has to pay to the hotel owner
Solution:
If VAT is included in the price, find the original price of each of the following.
