Ratio - Study Mode
[#256] Two numbers are in ratio 4 : 5 and their LCM is 180. The smaller number is
Correct Answer
(C) 36
Explanation
Solution: Let two numbers be 4x and 5x Their LCM = 180 and HCF = x Now, 1 st number × 2 nd number = LCM × HCF Or, 4x × 5x = 180 × x Or, 20x = 180 Or, x = 9 Then, the smaller number = 4 × 9 = 36
[#257] If x runs scored by A, y runs by B and z runs by C, then x : y = y : z = 3 : 2. If total number of runs scored by A, B and C is 342, the runs scored by each would be respectively = ?
Correct Answer
(B) 162, 108, 72
Explanation
Solution: Given, X : Y = 3 : 2 Y : Z = 3 : 2 Equal the value of Y in both equation X : Y = 3 : 2 (multiply with 3) and Y : Z = 3 : 2 (multiply with 2) i.e. X : Y = 9 : 6 and Y : Z = 6 : 4 ∴ X : Y : Z = 9 : 6 : 4 Total Run scored by A, B and C = 342 Run Scored by A = $$frac{9}{19} imes 342 = 162$$ Run Scored by B = $$frac{6}{19} imes 342 = 108$$ Run Scored by C = $$frac{4}{19} imes 342 = 72$$
[#258] Find the fraction which will bear the same ratio to $$frac{1}{27}$$ that $$frac{3}{11}$$ does to $$frac{5}{9}$$
Correct Answer
(A) $$frac{1}{{55}}$$
Explanation
Solution: $$eqalign{
& = x:frac{1}{{27}}::frac{3}{{11}}:frac{5}{9} cr
& Rightarrow frac{5}{9}x = frac{1}{{27}} imes frac{3}{{11}} = frac{1}{{99}} cr
& Rightarrow x = frac{1}{{99}} imes frac{9}{5} cr
& ,,,,,,,,,,,, = frac{1}{{55}} cr} $$
[#259] A, B, C and D have Rs. 40, Rs. 50, Rs. 60 and Rs. 70 respectively when they go to visit a fair. A spends Rs. 18, B spends Rs. 21, C spends Rs. 24 and D spends Rs. 27. Who has done the highest expenditure proportionate to his resources ?
Correct Answer
(A) A
Explanation
Solution: Ratio of the expenditures of A, B, C, D are as under: $$eqalign{
& { ext{A}} o frac{{18}}{{40}} = frac{9}{{20}} = 0.45 cr
& { ext{B}} o frac{{21}}{{50}} = 0.42 cr
& { ext{C}} o frac{{24}}{{60}} = 0.4 cr
& { ext{D}} o frac{{27}}{7} = 0.385 cr} $$ Clearly, A has done the highest expenditure proportionate to his resources.
[#260] Seema and Meena divide a sum of Rs. 25000 in the ratio of 3 : 2 respectively. If Rs. 5000 is added to each of their shares, what would be in the new ratio formed ?
Correct Answer
(D) 4 : 3
Explanation
Solution: $$eqalign{
& { ext{Seema's share}} cr
& = { ext{Rs}}{ ext{.}}left( {25000 imes frac{3}{5}}
ight) cr
& = { ext{Rs}}.15000. cr
& { ext{Meena's share}} cr
& = { ext{Rs}}{ ext{.}}left( {25000 imes frac{2}{5}}
ight) cr
& = { ext{Rs}}.10000. cr} $$ ∴ Required ration = (15000 + 5000) : (10000 + 5000) = 4 : 3