Ratio - Study Mode

[#91] What number has to be added to the terms 3 : 5 to make the ratio 5 : 6 ?
Correct Answer

(B) 7

Explanation

Solution: Let the number to be added be x Then, $$eqalign{
& = frac{{3 + x}}{{5 + x}} = frac{5}{6} cr
& Rightarrow 6left( {3 + x}
ight) = 5left( {5 + x}
ight) cr
& Rightarrow 18 + 6x = 25 + 5x cr
& Rightarrow x = 7 cr} $$

[#92] The ratio of the number of ladies to that of gents at a party was 3 : 2. When 20 more gents joined the party, the ratio was reversed. The number of ladies present at the party was -
Correct Answer

(B) 24

Explanation

Solution: Let the number of ladies and gents at the party be 3x and 2x respectively. Then, $$eqalign{
& = frac{{3x}}{{2x + 20}} = frac{2}{3} cr
& Rightarrow 9x = 4x + 40 cr
& Rightarrow 5x = 40 cr
& Rightarrow x = 8 cr} $$ ∴ Number of ladies = 3 × 8 = 24

[#93] Total number of men, women and children working in a factory is 18. They earn Rs. 4000 in a day. If the sum of the wages of all men, all women and all children is in ratio of 18 : 10 : 12 and if the wages of an individual man, woman and child is in ratio 6 : 5 : 3, then how much a woman earn in a day?
Correct Answer

(C) Rs. 250

Explanation

Solution: Ratio of number of men, women and children,
$$eqalign{
& = frac{{18}}{6}:frac{{10}}{5}:frac{{12}}{3} cr
& = 3:2:4 cr} $$ Total (Men + Women + Children) = 18
3X + 2X + 4X = 18 9X = 18 X = 2 Hence, number of women = 2X = 2 × 2 = 4 Share of all women = $$frac{{10 imes 4000}}{{40}}$$ xa0= Rs. 1000 [18 + 10 + 12 = 40] Thus, share of each woman = $$frac{{1000}}{4}$$ = Rs. 250

[#94] A and B are two alloys in which ratios of gold and copper are 5 : 3 and 5 : 11 respectively. If these equally amount of two alloys are melted and made alloy C. What will be the ratio of gold and copper in alloy C?
Correct Answer

(C) 15 : 17

Explanation

Solution: Ratio of Gold and Copper in Alloy A = 5 : 3 Ratio of Gold and Copper in Alloy B = 5 : 11 Amount of Gold in Alloy A = $$frac{5}{8}$$ Amount of Gold In Alloy B = $$frac{5}{{16}}$$ Amount of Copper in A = $$frac{3}{8}$$ Amount of Copper in B = $$frac{{11}}{{16}}$$ Amount of Gold In C, = (Amount of gold in A + Amount of gold in B) = $$frac{5}{8}$$ + $$frac{5}{{16}}$$ = $$frac{{10 + 5}}{{16}}$$ = $$frac{{15}}{{16}}$$ Amount of Copper in C, = Amount of Copper in A + Amount of Copper in B = $$frac{3}{8}$$ + $$frac{{11}}{{16}}$$ = $$frac{{17}}{{16}}$$ So, Ratio of Gold and Copper in C, $$ = frac{{15}}{{16}}:frac{{17}}{{16}} = 15:17$$

[#95] A bag contains an equal number of one rupee, 50 paise and 25 paise coins. If the total value is Rs. 35, how many coins of each type are there?
Correct Answer

(C) 20

Explanation

Solution: Let X coins of each type of there Total Value = Rs. 35 Now, X + $$frac{{ ext{X}}}{2}$$ + $$frac{{ ext{X}}}{4}$$ = 35 4X + 2X + X = 140 7X = 140 X = 20