RATIO AND PROPORTION

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Ratio and Proportion

  1. If A: B =4:5 and B:C =6:7, let us find A:C

  2. If A: B=3:7 and B:c =8:5, let us find A:C

  3. If x: y=2:3 , let us write by calculating the value of (4x-y): (2x+3y)

  4. If x: y =7:4, let us show that (5x-by): (3x+11y) =11:65

  5. Let us write what should be added to each term of the ratio x: y to make the ratio P: q

  6. Let us see whether four number 2.5, -2, -5 and 4 are in proportion or not.

  7. If 6: x: 2:13, then let us write by calculating the value of x.

  8. If 8: y: 2:21, let us write by calculating, the value of y.

  9. Let us find the fourth proportional of 6,9,12.

  10. Let us write by calculating which number is to be added to each of 2,4,6 and 10 to make the sums proportional.

  11. Let us write by calculating which number is to be added to each of 12, 22, 42 and 72 to make the sums proportional.

  12. Let us find the 3rd proportional of 9 and 15.

  13. Let us find 3rd proportional of 2a2 and 3ab.

  14. Let us find proportional of 1/12 and 1/75.

  15. Talking the number of proportion 7: 3: 14:6, let us apply componendo and dividend of proportion.

  16. If a: b=c: d =e: f, let us prove that each ratio is equal to (a+c+e): (b+d+f)

  17. If a: b = c: d, let us prove that (a2+c2) (b2+d2)= (ab+cd)2

  18. If x: a = y: b = z : c, let us show that x3/a3+y3/b3+z3/c3= 3xyz/abc

  19. If a: b= b: c, let us show that (a+ b+ c) (a+b + c) = a2+ b2 + c

  1. If ay-bx/c=cx-az/b=bz-cy/a, let us prove that x/a=y/b=z/c

  1. If  bz+cy/a=cx+az/b=ay+bx/c, let us prove that x/a(b2+c2-a2)=y/b(c2+a2-b2)=z/c(a2+b2-c2)

  1. If x = 4ab/a+b, let us show that x+2a/x-2a + x+2b/x-2b =2[ given a≠0,b≠0 and a≠b]

  2. If a+b-c/a+b=b+c-a/b+c=c+a-b/c+a and a+b+c ≠0, let us prove that a=b=c

  3. If bz-cy/b-c=cx-az/c-a, let us show that each ratio is equal to ay-bx/a-b

  4. If x/y+z=y/z+x + z/x+y , let us prove that each ratio is equal to 12 or (-1)

  5. If 2b/a+b=a+c-b/b+c-a=a+b+c/2a+b+2cwhere a+b+c≠0, letb us show that a/2=b/3=c/4

  6. If b+c-a/y+z-x=c+a-b/z+x-y=a+b-c/x+y-z, let us  prove that a/x=b/y=c/z

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