Ratio - Study Mode

[#176] Rs. 730 were divided among A,B,C in such a way that if A gets Rs. 3 then B gets Rs. 4 and If B gets Rs. 3.5 then C gets Rs. 3. The share of B exceeds that of C by = ?
Correct Answer

(B) Rs. 40

Explanation

Solution: A : B = 3 : 4 B : C = 3.5 : 3 = 7 : 6 A : B : C 3 : 4 7 : 6 21 : 28 : 24 A + B + C → 21 + 28 + 24 73 → 730 1 → 10 Then share of B exceeds that of C by (28 - 24) → 4 = 4 × 10 = 40

[#177] Among 132 examinees of a certain school, the ratio of successful to unsuccessful students is 9 : 2. Had 4 more students passed, then the ratio of successful to unsuccessful students will be = ?
Correct Answer

(D) 28 : 5

Explanation

Solution: Total Number of student = 132 The ratio of the pass : fail = 9 : 2 Number of student pass = $$frac{9}{11} imes 132 = 108$$ Number of student fail = $$frac{2}{11} imes 132 = 24$$ Now 4 student more passed. ∴ Number of student pass = 108 + 4 = 112 and, Number of student fail = 24 - 4 = 20 New ratio of pass : fail = 112 : 20 = 28 : 5

[#178] Last year, the ratio between the salaries of A and B was 3 : 4. But the ratios of their individual salaries between last year and this year were 4 : 5 and 2 : 3 respectively. If the sum of their present salaries is Rs. 4160, then how much is the salary of A now ?
Correct Answer

(B) Rs. 1600

Explanation

Solution: let the salaries of A and B last year be Rs. 3x and Rs. 4x respectively. Then, $$eqalign{
& { ext{A's present salary}} cr
& = { ext{Rs}}.left( {frac{5}{4} imes 3x}
ight) cr
& = { ext{Rs}}{ ext{.}}left( {frac{{15x}}{4}}
ight) cr
& { ext{B's present salary}} cr
& = { ext{Rs}}{ ext{.}}left( {frac{3}{2} imes 4x}
ight) cr
& = { ext{Rs}}.6x. cr
& herefore frac{{15x}}{4} + 6x = 4160 cr
& Rightarrow 39x = 4160 imes 4 cr
& Rightarrow x = frac{{4160 imes 4}}{{39}} cr
& { ext{So,}} cr
& { ext{A's present salary}} cr
& = { ext{Rs}}{ ext{.}}left( {frac{{15}}{4} imes frac{{4160 imes 4}}{{39}}}
ight) cr
& = { ext{Rs}}.1600 cr} $$

[#179] A and B are two alloys of gold and copper prepared by mixing metals in the ratio 7 : 2 and 7 : 11 respectively. If equal quantities of the alloys are melted to form a third alloy C, then the ratio of gold and copper in alloy C will be.
Correct Answer

(C) 7 : 5

Explanation

Solution: $$eqalign{
& { ext{Gold in C}} cr
& = left( {frac{7}{9} + frac{7}{{18}}}
ight),{ ext{units}} cr
& = frac{{ ext{7}}}{{ ext{6}}},{ ext{units}}{ ext{}} cr
& { ext{Copper in C}} cr
& = left( {frac{2}{9} + frac{{11}}{{18}}}
ight),{ ext{units}} cr
& = frac{5}{6},{ ext{units}}{ ext{}} cr
& herefore { ext{Gold}}:{ ext{Copper}} cr
& = frac{7}{6}:frac{5}{6} cr
& = 7:5 cr} $$

[#180] Two glasses of equal volume respectively are half and three - fourths filled with milk. They are then filled to brim by adding water. Their contents are then poured into another vessel. What will be the ratio of milk to water in this vessel ?
Correct Answer

(D) 5 : 3

Explanation

Solution: $$eqalign{
& { ext{Milk in 1st glass}} cr
& = frac{1}{2}{ ext{ unit}} cr
& { ext{Milk in 2nd glass}} cr
& = frac{3}{4}{ ext{ unit}} cr
& { ext{Water in 1st glass}} cr
& = frac{1}{2}{ ext{ unit}} cr
& { ext{Water in 2nd glass}} cr
& = frac{1}{4}{ ext{ unit}}{ ext{}} cr
& herefore { ext{Required ratio}} cr
& = frac{{frac{1}{2} + frac{3}{4}}}{{frac{1}{2} + frac{1}{4}}} cr
& = frac{5}{4} imes frac{4}{3} cr
& = 5:3 cr} $$