A vessel contains a mixture of apple, orange and mango juices in the respective ratio of 3 : 5 : 4. 12 litre of this mixture is taken out and 8 litre of apple juice is added to the mixture. If the respective quantities of apple juice and orange juice in the vessel are equal, what was the initial quantity of mixture in the vessel? (in litre)
Suppose, the initial quantity of mixture in vessel
=3x+5x+4x=12x
The quantity of apple juice in 12 litre of mixture
= 3 litre
The quantity of orange juice in 12 litre of mixtrue
= 5 litre
∴ The quantity of mango juice in 12 litre of mixture
= 4 litre
According to question,
3x-3+8=5x-5
2x=10
x=5 litre
The average salary of A, B and C is INR 7200/- , The average salary of B,C and D is INR 7550/-, If D’s salary is 25% more than A’s salary, what is the average of B and C’s salary
A+B+C= 7200×3=21600 ...(i)
B+C+D= 7500×3=22650 ...(ii)
D=A×125/100
4D=5A
From equation (i) and (ii).
D-A=1050
From equation(iii).
5A/4-A=1050
A=INR 4200/-
Putting the value of A in equation (i).
4200+B+C=21600
B+C=17400
∴ Average of B and C's salary
=17400/2=INR 8700/-
B is 8 years elder to A and B is also 8 years younger to C. 12 years hence, the respective ratio between the ages of A and C will be 5 : 9. What is the sum of present ages of A, B and C
Let the present age of A = x years
Age of B = (x+8) years
And age of C=(x+16) years
x+12/x+16+12=5/9
9x+108=5x+140
4x=32
x=8 years
Age of A = 8 years
Age of B = 16 years
Age of C = 24 years
∴ Sum of present ages of A, B and C
= 8+16+24
=48 years
If the volume and curved surface area of a cylinder are 462 m3 and 264 m2 respecively, what is the total surface area of the cylinder ? (in m2)
Volume of cylinder =πr2h
Curved surface area of cylinder = 2πrh
πr2h/2πrh= 462/264
r=2×1.75
r=3.5 m
πr2h=462
h = 462/πr2
=462×7/22×3.5×3.5
h=12 m
∴ Total surface area of the cylinder = 2πr (r+h
= 2×22/7×3.5(3.5+12)
=2387/7=341 m2
The time taken by a boat to travel a distance downstream is half the time taken by it to travel the same distance upstream. What is the speed of the boat downstream if it travels 7.5 km upstream in 1 hour 30 min ? (in km/h)
Time taken by boat upstream = 1 1/2
=3/2 hour
Time taken by boat downstream
= 3/2×1/2=3/4 hour
∴ Speed of boat downstream
=7.5×4/3 = 10 km/h
The respective ratio of the sums invested for 2 years each, in Scheme A offering 20% p.a. compound interest (compounded annually) and in Scheme B offering 9% p.a. simple interest is 1 : 3. Difference between the interests earned from both the schemes is INR 1200/- . How much was invested in Scheme A
Amount invested in scheme A = INR x
Amount invested in scheme B = INR 3x
3x×2×9/100x[(1+20/100)2-1]=1200
⇒ 54x/100-x[36/25-1]=1200
⇒ 54x/100-11x/25=1200
⇒ 54x-44x/100=1200
⇒ 10x=1200x100
⇒ x=INR 12000/-
‘B’ is 3 years elder to ‘A’ and ‘B’ is also 3 years younger to ‘C’. 3 years hence, the respective ratio between the ages of A and C will be 4:5. What is the sum of the present ages of A, B and C
Present age of C = (x+6) years
According to question
x+3/x+6+3= 4/5
⇒ 5x+15=4x+36
⇒ x=21 years
∴ The sum of the present ages of A, B and C
= x+x+3+x+6= 3x+9
=3×21+9= 63+9=72 years
To reach point B from point A, at 4 pm, Sara will have to travel at an average speed of 18 km/h. She will reach point B at 3 pm if she travels at an average speed of 24 km/h. At what average speed should Sara travel to reach point B at 2 pm
Let the distance between A and B =d km
d/18-d/24 = 1
4d-3d/72=1
d= 72 km
Time taken by Sara with the speed of 18 km/h
= 72/18 = 4 hour
∴ Required speed = 72/4-2 = 72/2 = 36 km/ h
A bag contains 6 red balls, 11 yellow balls and 5 pink balls, If two balls are drawn at random from the bag, one after another, what is the probability that first ball is red and the second ball is yellow
Probability that first ball is red = 6/22= 3/11
Probability that second ball is yellow = 11/21
∴ Required probability = 3/11×11/21= 1/7
The respective ratio between the speed of the boat upstream and speed of the boat downstream is 2:3. What is the speed of the boat in still water if it covers 42 km downstream in 2 hours 20 minutes ? (in km/h)
Speed of boat downstream = 42/2+(20/60)=42/2+(1/3)
=42×3/6+1=42×3/7
=18 km/h
∴ Speed of boat upstream = 18×2/3= 12 km/h
∴ Speed of boat in still water
=Speed downstream+speed of boat upstream/2
=12+18/2=15 km/h