Today our topic of discussion is Algebraic Ratio and Proportion Exercises11.2.
Algebraic Ratio and Proportion Exercises11.2
Exercise 11.2
- If a, b, c are continued proportional, which one of the followings is correct?
1) a ² = bc
3) ab= bc
2) b² = ac
4) a=b=c
- The ratio of ages of Arif and Akib is 5: 3. If Arif is of 20 years old, how many years later the ratio of their ages will be 7: 5?
1) 5 years
2) 6 years
3) 8 years
4) 10 years
- If the sides of a square double, how much will the area of a square be increased?
1) 2 times
3) 4 times
2) 3 times
4) 6 times:
- If x : y = 7:5, y :z = 5:7 then = how much?
1) 35:49
2) 35:35
3) 25:49
4) 49:25
- If b, a, c are continued proportional, then-
(i) a² = bc
(ii) b/a = c/a
(iii) (a + b)/(a – b) = (c + a)/(c – a)
Which one of the following is correct?
1) i
2) i and ii
3) i and iii
4) i, ii and iii
- If x : y = 2:1 and y : z = 2:1 ,then
(i) x, y, z are continued proportional
(ii) z / x = 1/4
(iii) y² + zx = 4yz
Which one of the following is correct?
1) i and ii
2) i and iii
3) ii and iii
4) i, ii and iii
- If * a/x = (m² + n²)/(2mn) then (√(a + x))/(√(a – x)) = what?
1) m/n
2) (m + n)/(m – n)
3) (m – n)/(m + n)
4) n/m
If the perimeter of a triangle is 36 cm and the ratio of length of its side is 3:45, then answer question 8 and 9:
- What is the length of its greatest side in c m?
1) 5
2) 9
3) 12
4) 15
- What is the area of the triangle in square cm?
1) 6
2) 54
3) 67
4) 90
- Weight of 1 cubic c.m wood is 7 decigram. What is the percentage of weight of the wood to the weight of equal volume of water?
- Distribute Tk. 300 among a, b, c, d in such a way that the ratios are a’s part : b’s part = 2:3, b’s part: c’s part = 1:2 and c’s part: d’s part 3: 2.
- Three fishermen have caught 690 pieces of fishes. The ratios of their parts 2/3, 4/5 and 5/6. How many fishes will each of them get?
- The perimeter of a triangle is 45 cm. The ratio of the lengths of the sides is 3:5:7. Find the length of each sides.
- If the ratio of two numbers is 5: 7 and their H.C.F. is 4, what is L.C.M. of the numbers?
- In a cricket game, the total runs scored by Sakib, Mushfique and Mashrafi were 171. The ratio of runs scored by Sakib and Mushfique, and Mushfique and Mashrafi was 3: 2. What were the runs scored by them individually?
- In an office, there were 2 officers, 7 clarks and 3 bearers. If a bearer gets Tk. 1, a clerk gets Tk. 2 and an officer gets Tk. 4. Their total salary is Tk. 150,000. What is their individual salary?
- If the sides of a square are increased by 20%, what is percentage of increment of the area of the square?
- If the length of a rectangle is increased by 10% and the breadth is decreased by 10%, what is the percentage of increase or decrease of the area of the rectangle?
- In a field, the ratio of production is 4: 7 before and after irrigation. In that field, the production of paddy in a land previously was 304 quintal. What would be the production of paddy after irrigation?
- If the ratio of paddy and rice produced from paddy is 3: 2 and the ratio of wheat and suzi produced from wheat is 4: 3, find the ratio of rice and suzi produced from equal quantity of rice and wheat.
- The area of a land is 432 square metre. If the ratios of lengths and breadths of that land and that of another land are 3: 4 and 2 : 5 respectively, then what is the area of another land?
- Zami and Simi take loans of different amounts at the rate of 10% simple profit on the same day from the same Bank. The amount on capital and profit which Zami refunds after 2 years is the the same amount that Simi refunds after 3 years on capital and profit. Find the ratio of their loan.
- The ratio of sides of a triangle is 5: 12: 13 and perimeter is 30 cm.
1) Draw the triangle and write down the type of triangle with respect to the angles.
2) Determine the area of a square drawn with the diagonal of a rectangle, where the the length of the rectangle is the largest side of the triangle and the breadth of the triangle is the smallest side of the triangle.
3) If the length is increased by 10% and the breadth is increased by 20%, what will be percentage of increase of the area?
- The ratio of present and absent students of a day in a class is 1 : 4.
1) Express the percentage of absent students against total students.
2) The ratio of present and absent students would be 1 9, if 5 more students were present. What was the total number of students?
3) Of the total number of students, the number of male students is 10 less than the twice of the number of female students. Find the ratio of male and female students.
- Ashik, Mizan, Anika and Ahona started a business with a total capital of Tk. 1,32,500 and had a profit of Tk. 26500 after the end of a year. In the capital of that business, Ashik’s part: Mizan’s part 2: 3, Mizan’s part: Anika’s part = 4:5 and Anika’s part: Ahona’s part = 5: 6.
1) Determine the simple ratio of the capital.
2) Determine the amount of capital of each person in that business.
3) 60% of the profit is invested in the business at the end of year. If the remaining profit is divided according to the capital ratio, then between Ahona and Ashik who will get the greater amount of profit money?
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