Algebraic Ratio and Proportion Exercises 11.1

Today our topic of discussion is Algebraic Ratio and Proportion Exercises 11.1.

Algebraic Ratio and Proportion Exercises 11.1

 

 

Exercise 11.1

1. If the sides of two squares are a and b metre respectively, what will be the ratio of their areas?
2. If the area of a circle is equal to the area of a square, find the ratio of their perimeter.

3. If the ratio of two numbers is 3: 4 and their L.C.M. is 180, find out the two numbers.
4. The ratio of absent and present students of a day in your class is found to be 1 : 4. Express the number of absent students in percentage with respect to the total number of students.
5. A thing is first bought and then sold with 28% loss. Find the ratio of buying and selling cost.
6. Sum of the ages of father and son is 70 years. 7 years ago the ratio of their ages were 5: 2. What will the ratio of their ages after 5 years?

7. If a:b = b:c, prove that,

1) a/c = (a ² + b²)/(b² + c²)

2) a² * b²* c² * (1/(a³) + 1/(b³) + 1/(c³)) = a³ + b³ + c³

3) (abc * (a + b + c)³)/((ab + bc + ca) ³) = 1

8. Solve:

1) (1 – √(1 – x))/(1 + √(1 – x)) = 1/3

2) (a + x – √(a² – x²))/(a + x + √(a²– x²)) = b/x,  2a > b > 0 and x ≠0

3) 81 * ((1 – x)/(1 + x)) ³ = (1 + x)/(1 – x)

9. if a/b = b/c = c/d show that,

1) (a³+ b³)/(b³ + c³) = (b³ + c³)/(c³ + d³)

2) (a² + b ² + c ²)(b² + c ² + d²) = (ab + bc + cd)²

 

 

10. If x = (4ab)/(a + b) show that, (x + 2a)/(x – 2a) + (x + 2b)/(x – 2b) = 2 a ne b
11. If x = (³√ (m + 1) +³√ (m – 1)/(³√ (m + 1) – ³√ (m – 1)) prove that, x³ – 3m * x²  + 3x – m = 0

12. If x = (√(2a + 3b) + √(2a – 3b))/(√(2a + 3b) – √(2a – 3b) show that, 3b * x² – 4ax + 3b = 0 .
13. (a² + b²)/(b²+ c²) = ((a + b) ²)/((b + c)²) show that, a, b, c are continued proportion.

14. If x/(b + c) = y/(c + a) = z/(a + b) prove that, a/(y + z – x) = b/(z + x – y) = c/(x + y – z)
15. 15.(bz – cy)/a = (cx – az)/b = (ay – bx)/c prove that, x/a = y/b = z/c
16. 16.If * (a + b – c)/(a + b) = (b + c – a)/(b + c) = (c + a – b)/(c + a) and a + b +c ne0 , prove that, a = b = c

17. If * x/(xa + yb + zc) = y/(ya + zb + xc) = z/za+xb+yc and x+y+z ≠0,show that each of the ratio is = 1/(a + b + c) 
18. If(a + b + c) * p = (b + c – a) * q = (c + a – b) * r = (a + b – c) * s , then prove that, 1/q + 1/r + 1/s = 1/p
19. If lx my nz, then show that = (x²)/(yz) + (y²)/(zx) + (z²)/(xy) = (mn)/(l²) + (nl)/(m ²) + (lm)/(n²)
20. If * p/q = (a²)/(b ²) and a/b = (√(a + q))/(√(a – q)) show that, (p + q)/a = (p – q)/q

 

 

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