Ratio - Study Mode
[#106] In an alloy, the ratio of copper and zinc is 5 : 2. If 1.250 kg of zinc is mixed in 17 kg 500 gm of alloy, then the ratio of copper and zinc will be = ?
Correct Answer
(A) 2 : 1
Explanation
Solution: The ratio of copper and zinc is 5 : 2 i.e 5x : 2x Quantity of initial mixture = 17.5 kg ∴ 5x + 2x = $$frac{35}{2}$$ ⇒ x = $$frac{5}{2}$$ Quantity of Copper in initial mixture $$eqalign{
& = frac{5}{2} imes 5 cr
& = frac{{25}}{2}kg cr} $$ Quantity of Zinc in initial mixture $$eqalign{
& = frac{5}{2} imes 2 cr
& = 5,kg cr} $$ Now after adding 1.250 kg of zinc = 5 + 1.250 = 6.250 kg = $$frac{{25}}{4}kg$$ ∴ New Ratio of copper : zinc $$eqalign{
& = frac{{25}}{2}:frac{{25}}{4} cr
& = 2:1 cr} $$
[#107] The income of A, B and C are in the ratio 7 : 9 : 12 and their spending are in the ratio 8 : 9 : 15. If A saves $$frac{1}{4}$$ th of his income then the savings of A, B and C are in the ratio of = ?
Correct Answer
(A) 56 : 99 : 69
Explanation
Solution: Let income of A, B and C are 7x, 9x and 12x respectively and expenditure of A, B and C are 8y, 9y and 15y respectively $$eqalign{
& Rightarrow { ext{Income}},{ ext{of,}} cr
& A imes frac{1}{4} = { ext{Saving}},{ ext{of}},{ ext{A}},left( {{ ext{given}}}
ight) cr
& Rightarrow 7x - 8y = 7x imes frac{1}{4} cr
& Rightarrow 28x - 32y = 7x cr
& Rightarrow 21x = 32y cr
& Rightarrow x:y = 32:21 cr} $$ ∴ The ratio of savings of A, B and C ⇒ (7x - 8y) : (9x - 9y) : (12x - 15y) ⇒ (7 × 32 - 8 × 21) : (9 × 32 - 9 × 21) : (12 × 32 - 15 × 21) ⇒ (224 - 168) : (288 - 189) : (384 - 315) ⇒ 56 : 99 : 69
[#108] What will be the simplest form of the ratio 3 hours : 1 day?
Correct Answer
(C) 1 : 8
Explanation
Solution: 1 day = 24 hours. ∴ Given ration = 3 : 24 = 1 : 8
[#109] In a proportion the product of 1 st and 4 th terms is 40 and that of 2 nd and 3 rd terms is 2.5x. Then the value of x is.
Correct Answer
(A) 16
Explanation
Solution: Product of 1 st and 4 th terms (extremes) = product of 2 nd and 3 rd terms (means) $$eqalign{
& Rightarrow { ext{2}}{ ext{.5}}x = { ext{40}} cr
& Rightarrow x = frac{{40}}{{2.5}} = 16 cr} $$
[#110] If 20% of A = 30% of B = $$frac{1}{6}$$ of C, then A : B : C is -
Correct Answer
(D) 15 : 10 : 18
Explanation
Solution: $$eqalign{
& 20\% ,{ ext{of A}} = 30\% ,{ ext{of B}} = frac{1}{6}{ ext{of C}} cr
& Rightarrow frac{{20{ ext{A}}}}{{100}} = frac{{30{ ext{B}}}}{{100}} = frac{{ ext{C}}}{{ ext{6}}} cr
& Rightarrow frac{{ ext{A}}}{5} = frac{{3{ ext{B}}}}{{10}} = frac{C}{6} = k(say) cr
& Rightarrow A = 5K,,B = frac{{10k}}{3},,C = 6k cr
& herefore { ext{A}}:{ ext{B}}:{ ext{C}} = 5k:frac{{10k}}{3}:6k cr
& ,,,,,,,,,,,,,,,,,,,,,,,,,, = 5:frac{{10}}{3}:6 cr
& ,,,,,,,,,,,,,,,,,,,,,,,,,, = 15:10:18 cr} $$