Arrange the number a = $$\frac{7}{{10}},$$ b = $$\frac{5}{8},$$ c = $$\frac{2}{3}$$ in descending order = ?
(A) a > b > c
(B) a > c > b
(C) b > c > a
(D) c > b > a
Solution:
$$\eqalign{ & a = \frac{{7 \times 24}}{{10 \times 24}} = \frac{{168}}{{240}} \cr & b = \frac{{5 \times 30}}{{8 \times 30}} = \frac{{150}}{{240}} \cr & c = \frac{{2 \times 80}}{{3 \times 80}} = \frac{{160}}{{240}} \cr & {\text{The descending order}} \cr & {\text{ = }}a > c > b \cr} $$
293.
A sum of Rs. 1240 is distributed among A, B and C such that the ratio of amount received by A and B is 6 : 5 and that of B and C is 10 : 9 respectively. Find the share of C ?
(A) Rs. 480
(B) Rs. 360
(C) Rs. 400
(D) Rs. 630
Solution:
Given, A : B = 6 : 5 B : C = 10 : 9 A : B = 6 : 5 (multiply with 2) i.e. A : B = 12 : 10 ∴ A : B : C = 12 : 10 : 9 ⇒ 12x + 10x + 9x = 1280 ⇒ x = 40 ∴ Share of C = 9 × 40 = 360
294.
What is the third proportional to 16 and 24?
(A) 36
(B) 28
(C) 34
(D) 32
Solution:
Third proportional of 16 and 24 $$ = \frac{{{b^2}}}{a} = \frac{{24 \times 24}}{{16}} = 36$$
295.
y varies directly as (x + 3) and y = 8 when x = 1. What is the value of y when x = 2 ?
(A) 6
(B) 10
(C) 12
(D) 16
Solution:
y α (x + 3) ⇒ y = k (x + 3) for some constant k. When y = 8, x = 1, y = k (x + 3) ⇒ 8 = k (1 + 3) ⇒ k = 2 When x = 2, y = 2(x + 3) = 2(2 + 3) = 2 × 5 = 10
296.
The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?
A mixture contains alcohol and water in the ratio of 4 : 3. If 5 litres of water is added to the mixture the ratio becomes 4 : 5. The quantity of alcohol in the given mixture is = ?
(A) 3 litres
(B) 4 litres
(C) 15 litres
(D) 10 litres
Solution:
Alcohol : Water 4 : 3 Let 4x : 3x ∴ 5 litres of water is added to the mixture $$\eqalign{ & \Rightarrow \frac{{4x}}{{3x + 5}} = \frac{4}{5} \cr & \Rightarrow 20x = 12x + 20 \cr & \Rightarrow 8x = 20 \cr & \Rightarrow x = \frac{{20}}{8} \cr & \Rightarrow x = \frac{5}{2} \cr & {\text{Quantity of alcohol}} \cr & \Rightarrow {\text{4}} \times \frac{5}{2} = 10\,{\text{litres}} \cr} $$
298.
The sides of a triangle are in the ratio of 7 : 9 : 12. The difference between the length of largest and smaller sides is 15 c.m. The length of the largest sides would be = ?
(A) 36 cm
(B) 12 cm
(C) 60 cm
(D) 24 cm
Solution:
Sides of a triangle are in the ratio of 7 : 9 : 12 i.e. 7x : 9x : 12x Difference between the length of largest and smaller sides = 12x - 7x = 15 ⇒ x = 3 ∴ largest sides would be 12 × 3 = 36cm
299.
A vessel of capacity 2 litre has 25% alcohol and another vessel of capacity 6 litre had 40% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. what is the new concentration of mixture ?
(A) 29%
(B) 49%
(C) 31%
(D) 71%
Solution:
Amount of alcohol in first vessel, = 25% of 2 litre = 0.25 × 2 = 0.5 litre Amount of alcohol in second vessel, = 40% of 6 litre = 0.4 × 6 = 2.4 litre Total amount of alcohol out of 10 litres of mixture is 0.5 + 2.4 = 2.9 litre Thus, Concentration of the mixture is, $$\frac{{2.9 \times 100}}{{10}}$$ = 29%
300.
If x runs scored by A, y runs by B and z runs by C, then x : y = y : z = 3 : 2. If total number of runs scored by A, B and C is 342, the runs scored by each would be respectively = ?
(A) 144, 96, 64
(B) 162, 108, 72
(C) 180, 120, 80
(D) 189, 126, 84
Solution:
Given, X : Y = 3 : 2 Y : Z = 3 : 2 Equal the value of Y in both equation X : Y = 3 : 2 (multiply with 3) and Y : Z = 3 : 2 (multiply with 2) i.e. X : Y = 9 : 6 and Y : Z = 6 : 4 ∴ X : Y : Z = 9 : 6 : 4 Total Run scored by A, B and C = 342 Run Scored by A = $$\frac{9}{19} \times 342 = 162$$ Run Scored by B = $$\frac{6}{19} \times 342 = 108$$ Run Scored by C = $$\frac{4}{19} \times 342 = 72$$