Ratio - Study Mode
[#136] There are three numbers A, B, C such that twice A is equal to thrice B and four times B is equal to five times C. Then the ratio between A and C is = ?
Correct Answer
(C) 15 : 8
Explanation
Solution: Given 2A = 3B and 4B = 5C i.e. A : B = 3 : 2 B : C = 5 : 4 A : B = 3 : 2 (multiply with 5) and B : C = 5 : 4 (multiply with 2) i.e. A : B = 15 : 10 and B : C = 10 : 8 ∴ A : B : C = 15 : 12 : 8 ∴ A : C = 15 : 8
[#137] If a : b = b : c, then a 4 : b 4 would be equal to
Correct Answer
(B) a 2 : c 2
Explanation
Solution: $$eqalign{
& = frac{a}{b} = frac{b}{c} cr
& Rightarrow {b^2} = ac cr
& Rightarrow frac{{{a^4}}}{{{b^4}}} = frac{{{a^4}}}{{{{left( {ac}
ight)}^2}}} cr
& ,,,,,,,,,,,,,,, = frac{{{a^4}}}{{{a^2}{c^2}}} cr
& ,,,,,,,,,,,,,,, = frac{{{a^2}}}{{{c^2}}} cr
& Rightarrow {a^4}:{b^4} = {a^2}:{c^2} cr} $$
[#138] If (4x 2 - 3y 2 ) : (2x 2 + 5y 2 ) = 12 : 19, then x : y is
Correct Answer
(C) 3 : 2
Explanation
Solution: $$eqalign{
& { ext{ = }}frac{{4{x^2} - 3{y^2}}}{{2{x^2} + 5{y^2}}} = frac{{12}}{{19}} cr
& Rightarrow 19left( {4{x^2} - 3{y^2}}
ight) = 12left( {2{x^2} + 5{y^2}}
ight) cr
& Rightarrow 76{x^2} - 57{y^2} = 24{x^2} + 60{y^2} cr
& Rightarrow 52{x^2} = 117{y^2} cr
& Rightarrow 4{x^2} = 9{y^2} cr
& Rightarrow frac{{{x^2}}}{{{y^2}}} = frac{9}{4} cr
& Rightarrow {left( {frac{x}{y}}
ight)^2} = {left( {frac{3}{2}}
ight)^2} cr
& Rightarrow frac{x}{y} = frac{3}{2} cr
& herefore x:y = 3:2 cr} $$
[#139] If x : y = 3 : 4 and a : b = 1 : 2, then the value of $$frac{{2xa + yb}}{{3yb - 4xa}}$$ xa0 is
Correct Answer
(D) $$frac{7}{6}$$
Explanation
Solution: $$eqalign{
& = frac{x}{y} = frac{3}{4}{ ext{ and }}frac{a}{b} = frac{1}{2} cr
& Rightarrow frac{{xa}}{{yb}} = frac{3}{4} imes frac{1}{2} = frac{3}{8} cr
& frac{{2xa + yb}}{{3yb - 4xa}} cr
& = frac{{2left( {frac{{xa}}{{yb}}}
ight) + 1}}{{3 - 4left( {frac{{xa}}{{yb}}}
ight)}} cr
& = frac{{2 imes frac{3}{8} + 1}}{{3 - 4 imes frac{3}{8}}} cr
& = frac{7}{4} imes frac{2}{3} cr
& = frac{7}{6} cr} $$
[#140] Income of A and B are in the ratio 4 : 3 and their annual expenses are in the ratio 3 : 2. If each save Rs. 60000 at the end of the year, the annual income of A is = ?
Correct Answer
(C) Rs. 240000
Explanation
Solution: A : B Income 4x : 3x Expenses 3y : 2y Saving 6000 : 6000 Income = Expenses + Saving $$ herefore frac{{4x - 60000}}{{3x - 60000}} = frac{3}{2}$$ ⇒ 8x - 120000 = 9x - 180000 ⇒ x = 60000 ∴ Income of A = 4 × 60000 = 240000