Ratio - Study Mode
[#71] Find the fraction which bears the same ratio to $$frac{1}{{27}}$$ that $$frac{3}{7}$$ does to $$frac{5}{9}$$ = ?
Correct Answer
(B) $$frac{1}{{35}}$$
Explanation
Solution: $$eqalign{
& { ext{Let the fraction is }}x cr
& Rightarrow x:frac{1}{{27}}::frac{3}{7}:frac{5}{9} cr
& Rightarrow frac{x}{{frac{1}{{27}}}} = frac{{frac{3}{7}}}{{frac{5}{9}}} cr
& Rightarrow 27x = frac{{3 imes 9}}{{7 imes 5}} cr
& Rightarrow x = frac{1}{{35}} cr} $$
[#72] The respective ratio between the monthly salaries of Rene and Som is 5 : 3. Out of her salary Rene gives $$frac{{ ext{1}}}{{ ext{6}}}$$ th as rent, $$frac{{ ext{1}}}{{ ext{5}}}$$ th to her mother, 30% as her education loan and keeps 25% aside for miscellaneous expenditure. Remaining Rs. 5000 she keeps as savings. What is Som's monthly salary ?
Correct Answer
(D) Rs. 36000
Explanation
Solution: Let the monthly salaries of Rene and Som be 5a and 3a respectively. Money spent by Rene $$ = left( {frac{1}{6}{ ext{of }}5a + frac{1}{5}{ ext{of }}5a + 30\% { ext{ of }}5a + 25\% { ext{ of }}5a}
ight)$$ According to given information $$ Rightarrow 5a - $$ $$left[ {5a imes frac{1}{6} + 5a imes frac{1}{5} + 5a imes frac{3}{{10}} + frac{{5a}}{4}}
ight] = $$ xa0 xa0 xa0 $$ 5000$$ $$eqalign{
& Rightarrow 5a - left[ {frac{{5a}}{6} + a + frac{{3a}}{2} + frac{{5a}}{4}}
ight] = 5000 cr
& Rightarrow 5a - left( {frac{{55a}}{{12}}}
ight) = 5000 cr
& Rightarrow 60a - 55a = 60000 cr
& Rightarrow a = 12000 cr
& herefore { ext{Som's salary}} cr
& = 3 imes 12000 cr
& = { ext{Rs}}{ ext{. }}36000 cr} $$
[#73] The present ratio of ages of A and B is 4 : 5. 18 years ago, this ratio was 11 : 16. Find the sum total of their present ages.
Correct Answer
(A) 90 years
Explanation
Solution: Let present age of A and B be 4x and 5x 18 years ago their ages $$frac{{4x - 18}}{{5x - 18}} = frac{{11}}{{16}}$$ Or, 64x - 288 = 55x - 198 Or, 64x - 55x = -198 + 288 Or, 9x = 90 Or, x = $$frac{{90}}{9}$$ = 10 Sum of the present ages = 40 + 50 = 90 years
[#74] A dishonest milk man mixed 1 liter of water for every 3 liters of milk and thus made up 36 liters of milk. If he now adds 15 liters of milk to mixture, find the ratio of milk and water in the new mixture:
Correct Answer
(B) 14 : 3
Explanation
Solution: Quantity of milk and water in the 36 liter mixture 27 liter milk and 9 liter water Now, 15 liters milk is added then milk becomes 42 liters Now, ratio = 42 : 9 = 14 : 3
[#75] If the ratio of the ages of Maya and Chhaya is 6 : 5 at present, and fifteen years from now, the ratio will get changed to 9 : 8, then find Maya's present age.
Correct Answer
(B) 30 years
Explanation
Solution: Let Maya's and Chhaya's present age is 6x and 5x respectively And, $$frac{{6{ ext{x}} + 15}}{{5{ ext{x}} + 15}} = frac{9}{8}$$ Or, 48x + 120 = 45x = 135 Or, 3x = 15 Or, x = 5 Present age of Maya = 6x = 30