654.One year ago the ratio between Laxmans and Gopals salary was 3:4. The ratios of their individual salaries between last years and this years salaries are 4:5 and 2:3 respectively. At present the total of their salary is Rs.4290. The salary of Laxman now is :
Rs.1040
Rs.1650
Rs.2560
Rs.3120
Explanation:
Let the salaries of Laxman and Gopal one yer before be 3x and 4x.
Given that laxman's last year and present year salary are in the ratio 4:5
So his present salary =$\dfrac{5}{4} \times 3x $= $\dfrac{15x}{4}$
Also Gopal's last year and present year salary are in the ratio 2:3
So his present salary $\dfrac{3}{2} \times 4x $= 6x
But given that sum of the salaries = $\dfrac{15x}{4} +6x =4290$
=>$\dfrac{39x}{4} $ =4290
=>39x= $ 4290 \times 4 $ =440
Laxman's present salary = $\dfrac{15x}{4} $ =$ \dfrac{15}{4} \times 440 $=1650
Given that laxman's last year and present year salary are in the ratio 4:5
So his present salary =$\dfrac{5}{4} \times 3x $= $\dfrac{15x}{4}$
Also Gopal's last year and present year salary are in the ratio 2:3
So his present salary $\dfrac{3}{2} \times 4x $= 6x
But given that sum of the salaries = $\dfrac{15x}{4} +6x =4290$
=>$\dfrac{39x}{4} $ =4290
=>39x= $ 4290 \times 4 $ =440
Laxman's present salary = $\dfrac{15x}{4} $ =$ \dfrac{15}{4} \times 440 $=1650
655.The ratio between the ages of Kamala and Savitri is 6:5 and the sum of their ages is 44 years. The ratio of their ages after 8 years will be :
5 : 6
7 : 8
8 : 7
14:13
Explanation:
Let their ages be 4x and x years.
∵ 6x + 5x = 44
∴ x = 4
So their present ages are 24 years and 20 years
Ratio of their ages after 8 years = 32 : 28 = 8 : 7.
∵ 6x + 5x = 44
∴ x = 4
So their present ages are 24 years and 20 years
Ratio of their ages after 8 years = 32 : 28 = 8 : 7.
656.In a mixture of 60 litres, the ratio of milk and water is 2:1. What amount of water must be added to make the ratio 1:2?
42 litres
56 litres
60 litres
77 litres
Explanation:
Quantity of milk =60 x $\dfrac{2}{3} $ litres = 40 litres.
Quantity of water in it = (60 - 40) litres = 20 litres.
New ratio = 1 : 2
Let quantity of water to be added further be x litres.
Then, milk : water =[$\dfrac{40}{20 + x}$]
Now, [$\dfrac{40}{20 + x}$] = $\dfrac{1}{2} $
=> 20 + x = 80
=>x = 60.
Quantity of water to be added = 60 litres.
Quantity of water in it = (60 - 40) litres = 20 litres.
New ratio = 1 : 2
Let quantity of water to be added further be x litres.
Then, milk : water =[$\dfrac{40}{20 + x}$]
Now, [$\dfrac{40}{20 + x}$] = $\dfrac{1}{2} $
=> 20 + x = 80
=>x = 60.
Quantity of water to be added = 60 litres.
657.As money is to Bs money as 4:5 and Bs money is to Cs money as 2:3. If A has Rs.800, C has
Rs.1000
Rs.1200
Rs.1500
Rs.2000
Explanation:
A has ₹800
A:B = 4:5
800:B = 4:5
B = 1000
B:C = 2:3
1000:C = 2:3
C= 1500
Total money with A,B and C = 800 + 1000 + 1500 = 3300
A:B = 4:5
800:B = 4:5
B = 1000
B:C = 2:3
1000:C = 2:3
C= 1500
Total money with A,B and C = 800 + 1000 + 1500 = 3300
658.Vinay got thrice as many marks in Maths as in English. The proportion of his marks in Maths and History is 4:3. If his total marks in Maths, English and History are 250, what are his marks in English ?
120
90
40
80
Explanation:
M = 3E and M/H = 4/3
∴ H = 3/4 M = 3/4 x 3E = 9/4 E
Now M + E + H = 250
⇒ 3E + E + 9/4 E = 250
⇒ 25 E = 1000
∴ E = 40
∴ H = 3/4 M = 3/4 x 3E = 9/4 E
Now M + E + H = 250
⇒ 3E + E + 9/4 E = 250
⇒ 25 E = 1000
∴ E = 40
659.Gold is 19 times as heavy as water and copper 9 times as heavy as water. The ratio in which these two metals be mixed so that the mixture is 15 times as heavy as water is:
1 : 2
2 : 3
3 : 2
19: 135
Explanation:
Let the ration of gold and copper that taken be a:l
$\dfrac{19a + 9I}{a+I}$ = $\dfrac{15}{I}$
19a+9I = 15a+15I
19a-15a=15I-9I
4a=6I
2a=3I
$\dfrac{a}{I} $ = $\dfrac{3}{2}$
Gold and copper are taken in the ratio 3 : 2
$\dfrac{19a + 9I}{a+I}$ = $\dfrac{15}{I}$
19a+9I = 15a+15I
19a-15a=15I-9I
4a=6I
2a=3I
$\dfrac{a}{I} $ = $\dfrac{3}{2}$
Gold and copper are taken in the ratio 3 : 2
670.How many cubes of edges 2dm can be cut out of a meter cube?
50
64
216
125
Explanation:
1 * 1 * 1 = 2/10 * 2/10 * 2/10 * x
x = 125
x = 125
671.The edge of three cubes of metal is 3dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube?
3 dm
4 dm
5 dm
6 dm
Explanation:
First find the volume of each cube.
Cube A=3^3=27
Cube B=64
Cube C=125.
If they are melted and a new cube is formed, then the volume of this cube is equal to the sum of the volumes of the individual cubes.
So Volume of new cube= 216.
To find the edge of this cube, we find the cube root of 216, as a^3=216, we have a=cu.root of 216.
So the answer is 6dm.
Cube A=3^3=27
Cube B=64
Cube C=125.
If they are melted and a new cube is formed, then the volume of this cube is equal to the sum of the volumes of the individual cubes.
So Volume of new cube= 216.
To find the edge of this cube, we find the cube root of 216, as a^3=216, we have a=cu.root of 216.
So the answer is 6dm.
672.The slant height of a cone is 12 cm and radius of the base is 4cm, find the curved surface of the cone?
74 π cm2
36 π cm2
48 π cm2
24 π cm2
Explanation:
Curved surface of the cone = $\pi \times base \times height $
=> $\pi \times 4 \times 12 $
=>$48 \pi cm^{2} $
=> $\pi \times 4 \times 12 $
=>$48 \pi cm^{2} $
673.The ratio between the radii of two spheres is 1:3. Find the ratio between their volumes?
27:1
1:27
1:9
9:1
Explanation:
the ratio between the radii of two spheres is 1 : 3.
we know, volume of sphere = 4/3 πr³
⇒volume of sphere ∝ (radius)³
so, volume of sphere₁/volume of sphere₂ = (r₁/r₂)³
= (1/3)³
= 1³/3³
= 1/27
hence ratio of volume of spheres is 1 : 27.
we know, volume of sphere = 4/3 πr³
⇒volume of sphere ∝ (radius)³
so, volume of sphere₁/volume of sphere₂ = (r₁/r₂)³
= (1/3)³
= 1³/3³
= 1/27
hence ratio of volume of spheres is 1 : 27.
676.A man whose speed is 4.5 kmph in water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
8 kmph
4 kmph
2 kmph
10 kmph
679.An equilateral triangular plate is to be cut into n number of identical small equilateral triangular plates. Which of the following can be possible value of n?
196
216
256
296
682.The average of x1, x2, and x3, is 14. Twice the sum of x2 and x3 is 30. What is the value of x1 ?
20
27
16
2
686.The number of times in a day the hour-hand and the minute-hand of a clock are at right angles, is
44
48
24
12
687.An accurate clock shows the time as 3.00. After hour hand has moved 1350 , the time would be.
7.30
6.30
8.00
9.30
691.P, Q, R, S and T are five speakers who have to speak on a particular day, not necessarily in the same order, R is neither the first nor the last speaker. There are three speakers after S and three speakers ahead of T. if P speaks after Q, then who is the last speaker to speak?
S
T
P
Q
692.Five persons A, B, C, D and E are being compared in weight and height. The second heaviest person D is the shortest. A is the 2nd tallest and shorter than E, the heaviest person is the third tallest person. There is the only one person shorter than B, who is lighter than E and A respectively. Who is the heaviest person?
A
B
C
D
693.A, B, C, D, E, and F are six cities which are collinear in the same order. The distance between any two adjacent cities is equal. A bus starts at A for city F. It takes 25 minutes for the bus to travel from one city to another and stops for 5 minutes at each place. If the bus reaches E at 8.55, then at what time did it reach station B?
7:25
7:30
7:40
7:50
694.Four cars numbered as C1, C2, C3, and C4 are participating in a car rally. They have to travel from P to Q then to R. After the race, the following is observed.
i. The digit in the care number and the order in which they depart or arrive at any point is not the same.
ii. The first car to leave P is the second car to reach R.
iii. The first car to reach R is the second car to leave P and last car to reach Q
Which is the first car to leave P?
i. The digit in the care number and the order in which they depart or arrive at any point is not the same.
ii. The first car to leave P is the second car to reach R.
iii. The first car to reach R is the second car to leave P and last car to reach Q
Which is the first car to leave P?
C4
C3
C2
C1
695.B1, B2 and B 3 are the three buses that travel from Mumbai to Delhi. Each bus starts at a different time and arrives at different time. The digit in the bus number and the order of their departure of arrival is not the same. The first bus to leave Mumbai is the third bus to reach Delhi.
Which is the second bus to reach Delhi?
Which is the second bus to reach Delhi?
B1
B2
B3
B2 or B3