ICOME
    FOLLOW US: facebook twitter instagram youtube
JOIN ICOME
JOIN ICOME
JOIN ICOME

Welcome to ICOME Quiz Corner

Q1. If A:B = 1:2, B:C = 3:4 and C:D = 5:6, find A:B:C:D .

(a) 15:30:40:48 (b) 3:2:6:10 (c) 9:18:15:20 (d) 19:20:21:22

Solution.
A:B = 1:2

B:C = 3:4

= 2:(8/3)

C:D = 5:6

= (8/3):(16/15)

A:B:C:D = 1:2:(8/3):(16/15)

= 15:30:40:48
Solution

Q2. If a/b = 2/3 and b/c = 4/5 so find (a+b)/(b+c) .

(a) 9/8 (b) 10/9 (c) 20/27 (d) 15/16

(a+b)/(b+c) = [(a/b)+ 1]/[1 + (c/b)]

= [(2/3) + 1]/[1 + (5/4)]

= 20/27
Solution

Q3. If a:b = 2:1 , b:c = 3:4 , find the value of a2:b2:ac .

(a) 10:11:15 (b) 12:3:8 (c) 2:3:4 (d) 4:6:3

Solution.
a:b = 2:1

b:c = 3:4

a:b:c = 6:3:4

a2:b2:ac = 36:9:24

= 12:3:8
Solution

Q4. If 2A : 3B and 5B = 6C, find A:C .

(a) 3:7 (b) 4:3 (c) 5:9 (d) 9:5

Solution.
A/B = 3/2 , B/C = 6/5

A/C = A/B x B/C

= 3/2 x 6/5

= 18/10 = 9/5

A:C = 9:5
Solution

Q5. If p/4 = q/5 = r/9 , then (p+q+r)/p is .

(a) 3.5 (b) 4.5 (c) 4 (d) 5

Solution.
p/4 = q/5 = r/9 = k

p = 4k , q = 5k , r = 9k

= (4k+5k+9k)/4k

= 18k/4k

= 18/4 = 18/4

9/2 = 4.5
Solution

Q6. Seats for mathematics, statistics and physics in a Degree college are in the ratio 5:6:8. Under an expansion process college will increase seats by 20%, 50% and 50% respectively, what will be the increased ratio .

(a) 2:4:3 (b) 4:3:1 (c) 2:3:4 (d) 1:3:4

Solution.
= 5 + 20% of 5 : 6 + 50% of 6 : 8 + 50% of 8

= 6 : 9 : 12

= 2 : 3 : 4
Solution

Q7. What is the value of (a2 - b2)/(a + b)2 if a/b = 4

(a) 2/5 (b) 1/2 (c) 2/3 (d) 3/5

Solution.
(a2 - b2)/(a + b)2 = [(a-b)(a+b)]/(a+b)2 = (a-b)/(a+b)

= [(a/b)-1]/[(a/b)+1] = (4-1)/(4+1) = 3/5
Solution

Q8. If x = 51/3 + 5-1/3 , find the value of x3 - 3x .

(a) 26 (b) 5 (c) 26/5 (d) 1/5

Solution.
x = 51/3 + 5-1/3

x3 = ( 51/3 + 5-1/3)3

= 5 + 5-1 + 3.51/3 . 5-1/3(51/3 + 5-1/3 )

x3 = 5 + 1/5 + 3x

x3 - 3x = 26/5
Solution

Q9. If x1/3 + y1/3 + z1/3 = 0 , find the value of (x+y+z)3 .

(a) 1 (b) 3xyz (c) 27xyz (d) xyz

Solution.
x1/3 + y1/3 + z1/3 = 0

(x1/3)3 + (y1/3)3 + (z1/3)3 = 3x1/3.y1/3.z1/3

x + y + z = 3x1/3.y1/3.z1/3

(x + y + z)3 = (3x1/3.y1/3.z1/3)3 = 27xyz

Note : If x + y + z = 0 then x3 + y3 + z3 = 3abc
Solution

Q10. If a/b = c/d → (a+b)/b = (c+d)/d is called

(a) Dividendo (b) Altenendo (c) Invertendo (d) Componendo

Solution.
(d) Componendo
Solution