Ratio - Study Mode

[#216] If A : B = 3 : 4 and B : C = 8 : 9, then A : B : C is = ?
Correct Answer

(C) 6 : 8 : 9

Explanation

Solution: Given,
A : B = 3 : 4 B : C = 8 : 9 A : B = 3 : 4 (multiply with 2) i.e. A : B = 6 : 8 and B : C = 8 : 9 ∴ A : B : C = 6 : 8 : 9

[#217] If 2A = 3B = 4C, the A : B : C is = ?
Correct Answer

(C) 6 : 4 : 3

Explanation

Solution: $$eqalign{
& ,,,{ ext{A}},,,,,,,{ ext{:}},,,,,,{ ext{B}},,,,,,{ ext{:}},,,,,{ ext{C}} cr
& 3 imes 4:2 imes 4:2 imes 3 cr
& ,,,12,,,,:,,,,,{ ext{8}},,,,,:,,,,{ ext{6}} cr
& ,,,x08oxed{,,6,,,,:,,,,4,,,,,,:,,,,3,,} cr} $$

[#218] x, y, z, u are real numbers such that x : y = y : z = z : u and x : u = 64 : 27. the value of x : z is -
Correct Answer

(B) 16 : 9

Explanation

Solution: $$eqalign{
& { ext{Let}},frac{x}{y} = frac{y}{z} = frac{z}{u} = k. cr
& { ext{Now, }}frac{x}{u} = frac{{64}}{{27}} cr
& Rightarrow frac{x}{y} imes frac{y}{z} imes frac{z}{u} = frac{{64}}{{27}} cr
& Rightarrow {k^3} = {left( {frac{4}{3}}
ight)^3} cr
& Rightarrow k = frac{4}{3}. cr
& { ext{So}},,x:y = y:z = z:u = 4:3. cr
& herefore frac{x}{z} = frac{x}{y} imes frac{y}{z} = frac{4}{3} imes frac{4}{3} = frac{{16}}{{9.}} cr} $$

[#219] If p : q : r = 1 : 2 : 4, then $$sqrt {5{p^2} + {q^2} + {r^2}} $$ xa0 xa0is equal to -
Correct Answer

(C) 5p

Explanation

Solution: $$eqalign{
& p = k,,q = 2k,,r = 4k cr
& { ext{Then,}} cr
& sqrt {5{p^2} + {q^2} + {r^2}} cr
& = sqrt {5{k^2} + {{left( {2k}
ight)}^2} + {{left( {4k}
ight)}^2}} cr
& = sqrt {5{k^2} + 4{k^2} + 16{k^2}} cr
& = sqrt {25{k^2}} cr
& = 5k cr
& = 5p. cr} $$

[#220] If A : B : C = 2 : 3 : 4, then the ratio $$frac{{ ext{A}}}{{ ext{B}}}$$ : $$frac{{ ext{B}}}{{ ext{C}}}$$ : $$frac{{ ext{C}}}{{ ext{A}}}$$ is equal to -
Correct Answer

(B) 8 : 9 : 24

Explanation

Solution: $$eqalign{
& { ext{let A}} = 2{ ext{k}},,{ ext{B}} = 3{ ext{k,}},{ ext{C}} = 4{ ext{k}} cr
& { ext{Then,}} cr
& Rightarrow frac{{ ext{A}}}{{ ext{B}}} = frac{{2{ ext{k}}}}{{3{ ext{k}}}} = frac{2}{3}, cr
& Rightarrow frac{{ ext{B}}}{{ ext{C}}} = frac{{3{ ext{k}}}}{{4{ ext{k}}}} = frac{3}{4}, cr
& Rightarrow frac{{ ext{C}}}{{ ext{A}}} = frac{{4{ ext{k}}}}{{2{ ext{k}}}} = 2 cr
& Rightarrow frac{{ ext{A}}}{{ ext{B}}}:frac{{ ext{B}}}{{ ext{C}}}:frac{{ ext{C}}}{{ ext{A}}} = frac{2}{3}:frac{3}{4}:2 cr
& = 8:9:24 cr} $$