Ratio - Study Mode
[#221] The current ages of Sonali and Monali are in the ratio 5 : 3. Five years from now, their ages will be in the ratio 10 : 7. Then Monali's current age is = ?
Correct Answer
(C) 9 years
Explanation
Solution: Let, ⇒ Sonali's age = 5x ⇒ Monali's age = 3x According to the question, $$eqalign{
& Rightarrow frac{{5x + 5}}{{3x + 5}} = frac{{10}}{7} cr
& Rightarrow frac{{x + 1}}{{3x + 5}} = frac{2}{7} cr
& Rightarrow 7x + 7 = 6x + 10 cr
& Rightarrow x = 3 cr} $$ ⇒ So, Monali's present age = 3x = 3 × 3 = 9 years
[#222] If $$frac{a}{b}{ ext{ = }}frac{c}{d}{ ext{ = }}frac{e}{f}{ ext{,}}$$ xa0 xa0then each of them is equal to = ?
Correct Answer
(D) $$frac{{a + 3c - 5e}}{{b + 3d - 5f}}$$
Explanation
Solution: $$eqalign{
& { ext{Let,}} cr
& frac{a}{b} = frac{c}{d} = frac{e}{f} = frac{1}{2} cr} $$ Now check from option to save your valuable time $$eqalign{
& { ext{Option D}} cr
& frac{{a + 3c - 5e}}{{b + 3d - 5f}} Rightarrow frac{c}{d}left[ {frac{{frac{a}{c} + 3 - frac{{5e}}{c}}}{{frac{b}{d} + 3 - frac{{5f}}{d}}}}
ight] cr
& Rightarrow frac{c}{d} = frac{1}{2}left( {{ ext{Satisfy}}}
ight) cr} $$
[#223] Present ages of A and B are in the ratio 5 : 6 respectively. After seven years this ratio becomes 6 : 7. Then the present age of A in years is = ?
Correct Answer
(A) 35 years
Explanation
Solution: Let the age of A & B = 5x and 6x years According to question, $$eqalign{
& frac{{5x + 7}}{{6x + 7}} = frac{6}{7} cr
& 35x + 49 = 36x + 42 cr
& x = 7 cr
& { ext{A's Present age}} = 5x cr
& = 5 imes 7 = { ext{35 years}} cr} $$
[#224] In a school the ratio of boys and girls is 4 : 5 respectively. When 100 girls leave the school the ratio becomes 6 : 7 respectively. How many boys are there in the school ?
Correct Answer
1300
Explanation
Solution: Let the number of boys and girls be 4x and 5x respectively. Then, $$eqalign{
& { ext{ = }}frac{{4x}}{{5x - 100}} = frac{6}{7} cr
& Rightarrow 28x = 30x - 600 cr
& Rightarrow 2x = 600 cr
& Rightarrow x = 300 cr
& herefore { ext{Number of boys}} cr
& = 4 imes 300 cr
& = 1200 cr} $$
[#225] One year ago the ratio of the ages of Sarika and Gouri was 3 : 4 respectively. One year hence the ratio of their ages will be 10 : 13 respectively. What is Sarika's present age ?
Correct Answer
18 years
Explanation
Solution: Let Sarika's and Gauri's ages one year ago be 3x and 4x years respectively Sarika's age 1 year hence = (3x + 2) years Gauri's age 1 year hence = (4x + 2) $$eqalign{
& herefore frac{{3x + 2}}{{4x + 2}} = frac{{10}}{{13}} cr
& Rightarrow 13left( {3x + 2}
ight) = 10left( {4x + 2}
ight) cr
& Rightarrow 39x + 26 = 40x + 20 cr
& Rightarrow x = 6 cr} $$ Hence, Sarika's present age = 3x + 1 = (3 × 6 + 1) years = 19 years