Ratio - Study Mode

[#126] Two numbers are in the ratio 3 : 5. If 6 is added to both of them, the ratio becomes 2 : 3. The numbers are = ?
Correct Answer

(D) 18 and 30

Explanation

Solution: Let numbers are = 3x and 5x ∴ According to question, $$eqalign{
& Rightarrow frac{{3x + 6}}{{5x + 6}} = frac{2}{3} cr
& Rightarrow 9x + 18 = 10x + 12 cr
& Rightarrow x = 6 cr
& { ext{So, numbers are }} cr
& 3x = 3 imes 6 = 18 cr
& 5x = 5 imes 6 = 30 cr} $$

[#127] The boys and girls in a college are in the ratio 3 : 2. If 20% of the boys and 25% of the girls are adults, the percentage of students who are not adults is -
Correct Answer

(C) 78%

Explanation

Solution: Let the number of boys and girls be 3x and 2x respectively Then, Number of boys and girls who are adults $$eqalign{
& = 20\% { ext{ of }}3x + 25\% { ext{ of }}2x cr
& = left( {frac{{20}}{{100}} imes 3x}
ight) + left( {frac{{25}}{{100}} imes 2x}
ight) cr
& = frac{3}{5}x + frac{x}{2} = frac{{11x}}{{10}} cr} $$ ∴ Number of boys and girls who are not adults $$eqalign{
& = left[ {left( {3x + 2x}
ight) - frac{{11x}}{{10}}}
ight] cr
& = 5x - frac{{11x}}{{10}} cr
& = frac{{39x}}{{10}} cr
& { ext{Required percentage}} cr
& = left( {frac{{39x}}{{10}} imes frac{1}{{5x}} imes 100}
ight)\% cr
& = 78\% cr} $$

[#128] The cost of a table and a chair are in the ratio of 5 : 7. If the cost of chair and table is increased by 20% and 10% respectively, then what will be the new ratio?
Correct Answer

(B) 55 : 84

Explanation

Solution: Let the cost of the table and chair be Rs. 5x and Rs. 7x respectively $$eqalign{
& { ext{New cost of chair}} cr
& = 120\% { ext{ of }}7x cr
& = { ext{Rs}}{ ext{.}}left( {frac{6}{5} imes 7x}
ight) cr
& = { ext{Rs}}{ ext{.}}frac{{42x}}{5} cr
& { ext{New cost of table}} cr
& = 110\% { ext{ of }}5x cr
& = { ext{Rs}}{ ext{.}}left( {frac{{11}}{{10}} imes 5x}
ight) cr
& = { ext{Rs}}{ ext{.}}frac{{55x}}{{10}}. cr
& herefore { ext{New ratio}} cr
& = frac{{55x}}{{10}}:frac{{42x}}{5} cr
& = 55:84 cr} $$

[#129] Ratio of earnings of A and B is 8 : 9 respectively. If the earnings of A increase by 50% and the earnings of B decrease by 25%, the new ratio of their earnings becomes 16 : 9 respectively. What are A's earnings?
Correct Answer

(D) Cannot be determine

Explanation

Solution: Let the earnings of A and B Rs. 8x and Rs. 9x respectively. Then, $$eqalign{
& = frac{{150\% { ext{ of }}8x}}{{75\% { ext{ of }}9x}} = frac{{16}}{9} cr
& Rightarrow frac{{frac{3}{2} imes 8x}}{{frac{3}{4} imes 9x}} = frac{{16}}{9} cr
& Rightarrow frac{{16}}{9} = frac{{16}}{9} cr} $$ Hence, A's earnings cannot be determined

[#130] A mixture contains spirit and water in the ratio of 3 : 2. If it contains 3 litres more spirit than water, the quantity of spirit in the mixture is = ?
Correct Answer

(C) 9 litres

Explanation

Solution: Spirit and Water in the ratio of 3 : 2 There are 3 liters more spirit in the mixture. ∴ 3x - 2x = 3 ⇒ x = 3 ∴ Quantity of spirit in the mixture = 3 × 3 = 9