Ratio - Study Mode

[#156] In a ratio which is equal to 7 : 8, if the antecedent is 35, what is the consequent?
Correct Answer

(B) 40

Explanation

Solution: Let the consequent be x $$eqalign{
& { ext{Then,}} cr
& frac{7}{8} = frac{{35}}{x} Rightarrow 35 imes 8 cr
& Rightarrow x = frac{{35 imes 8}}{7} = 40 cr} $$

[#157] If 8a = 9b then the ratio of $$frac{{ ext{a}}}{9}$$ to $$frac{{ ext{b}}}{8}$$ is
Correct Answer

(A) 1 : 1

Explanation

Solution: $$eqalign{
& = { ext{8a}} = { ext{9b}} Rightarrow a = frac{9}{8}b cr
& herefore frac{{ ext{a}}}{{ ext{9}}}:frac{{ ext{b}}}{{ ext{8}}} = frac{{left( {frac{9}{8}b}
ight)}}{9}:frac{{ ext{b}}}{{ ext{8}}} cr
& = frac{{ ext{b}}}{{ ext{8}}}:frac{{ ext{b}}}{{ ext{8}}} = 1:1 cr} $$

[#158] If x : y = 3 : 4, then (2x + 3y) : (3y - 2x) would be equal to.`
Correct Answer

(B) 3 : 1

Explanation

Solution: $$eqalign{
& = frac{x}{y} = frac{3}{4} cr
& = frac{{2x + 3y}}{{3y - 2x}} cr
& = frac{{2left( {frac{x}{y}}
ight) + 3}}{{3 - 2left( {frac{x}{y}}
ight)}} cr
& = frac{{2 imes frac{3}{4} + 3}}{{3 - 2 imes frac{3}{4}}} cr
& = frac{9}{2} imes frac{2}{3} = 3 cr
& = left( {2x + 3y}
ight):left( {3y - 2x}
ight) cr
& = 3:1 cr} $$

[#159] Rs. 33630 are divided among A, B and C in such a manner that the ratio of the amount of A to that of B is 3 : 7 and the ratio of the amount of B to that of C is 6 : 5. The amount of money received by B is = ?
Correct Answer

(A) Rs. 14868

Explanation

Solution: Given,
A : B = 3 : 7 B : C = 6 : 5 A : B = 3 : 7 (multiply with 6) and B : C = 6 : 5 (multiply with 7) i.e. A : B = 18 : 42 and B : C = 42 : 35 ∴ A : B : C = 18 : 42 : 35 ⇒18x + 42x + 35x = 33630 ⇒ x = 354 ∴ Money received by B = 42 × 354 = Rs. 14868

[#160] 200 litres of a mixture contains milk and water in the ratio 17 : 3. After the addition of some more milk to it, the ratio of milk to water in the resulting mixture becomes 7 : 1. The quantity of milk added to it was =?
Correct Answer

(B) 40 Litres

Explanation

Solution: Milk : water = 17 : 3 = 17x : 3x ∴ 17x + 3x = 200 ⇒ x =10 litre Milk = 170 litre and water = 30 litre in initial mixture. Let 'y' litre of milk added in mixture i.e. 170 + y : 30 = 7 : 1 ⇒ $$frac{{170 + y}}{{30}} = frac{7}{1}$$ ∴ y = 210 - 170 = 40 litre