Solution:
Let the ratio of two original numbers be 1 : x.
So (1+1)/(x+1) =B/C
and 3/( x+2) = ½
=>x= 4
So, 1/x= 1/A = ¼
So required Sum = 5.
Solution:
A:B:C= 5:6:3 =14
Let the profit be 100
=>profit shared = 70
=>Difference of profit between A&B+C,
(30+70*5/14) –( 70* 6/14 +70 *3/14) =200
55-45=200
ie )10 ——– *20 = 200
so total profit = 100 *20 =Rs.2000
Solution:
Ratio of investment = 48,000 : 80,000
=3:5
Profit of Ruhi ½ * 40/100 *16,800 +3/8 *60/100 *16,800
=3360 +3780
=Rs. 7,140
Solution:
Let the three numbers be 2x,3x and 4x
Then ( 2x+5) *3x= 21
=>2×2 + 5x-7 = 0
=>(2x+7)( x-1) = 0
=>x=1, -7/2
So the numbers are 2, 3, 4
So difference = 4-2 = 2
Solution:
Ratio of capitals = 5:6
Required difference = (6-5)/(6+5) * (88/100* 750 0) + 12/100 *7500
=600+900 = Rs.1500
Solution:
Let the radius of the cylinder be r cm.
Given h = 4r/6 cm
Volume of cylinder = 3888
r2 * 4r/ 6 = 3888
=>r3= 5832
=> r= 18 cm
Solution:
LCM ( 4, 6, 10,16) = 240
So ¼*240 = 80
1/6*240=40
1/10 *240 = 24
1/16*240=15
So total number of sweets= 80+ 40+24+15= 159
Solution:
Let the third friend age be x.
Then first friend age 140 % of x= 140x/100 = 7x/5
Second friend age = 150% of x= 150x/100 = 3x/2
So ratio= 7x/5: 3x/2 = 14x:15x= 14:15
Solution:
Let the base be x and y of two triangles.
Heights are 3h and 2h.
(½ X x X 3h) /( ½ X y X 2h) = 5/3
x/ y = 5/ 3 x 2/ 3 = 10/9 =>x:y= 10: 9
Solution: Ratio= 2 + 5 : 3+2 = 7: 5
Solution:
Let Pintu’s present age =x, Chintu = 2x and Mintu = x+2x =3x
Two years later [2x+2/3x+2] = (7/10)
20x+20=21x+14 = 6=x
Pintu’s present age =6
Five years ago, his age was 6-5= 1 year
Solution:
Ratio of speed is same as ratio of distance covered by them as speed and distance are directly proportional to each other. When time is constant.
A B C
(x/12)×11 (x/14)×12 (x/16)×14
Ratio is (11/12): (12/14): (14/16)
L.C.M of 12, 14, 16 is 336
=308:288:294 = 154:144:147
[What is x? Since distance covered by A in 12 steps is equal to distance covered by B in 14 steps and distance covered by C in 16 steps, hence let this distance =x. Distance covered in 1 step by A, B and C= (x/12), (x/14) and (x/16) respectively ]
Solution:
Let price =P, number of diamonds = n and weight of gold = g
When p=10000, n=64 and g=15, k=?
P= kg3√n => 10000 = k(15) (3√64)
K=(10000/15×4)=(500/3)
P=10500, g=21, k=(500/3), n=?
P=(500/3) g3√n => 10500=(500/3).213√n
3√n=10500×(3/500)×(1/21)=3=>n=27
Solution:
Container A Container B
Kerosene water Kerosene water
30 0 0 30
-10 –+10 –
20 0 10 30
When 10 litres of kerosene is taken out from A and put in B, then kerosene in A= 20 litres. Mixture in B= 40 litres in which ratio of Kerosene to water =10:30 = 1:3, when 12 litres of mixture is taken out from B, and put in A, then out of 12 litres
12×(1/4)=3 litres is kerosene and remaining 9 litres is water.
Container A Container B
Kerosene water Kerosene water
20 0 10 30
+3 +9-3 -9
23 9 -7 21
Ratio of Kerosene in A to B = 23:7
Solution:
Let the no. of students in class II be 5x and 3x respectively and contribution made by each student of class I and class II be 19y and 17y respectively.
Hence, ratio of total contribution of class I and class II =5x×19y: 3x×17y = 95:51
Total contribution made by students of class II (51/(95+51))×29200=10200
Solution:
Speed of the donkey, Without any load = 8 kmph. With 4 kgs of load, speed becomes 6 kmph, hence speed is reduced by 2 kmph.
Reduction in speed varies directly with the square root of the load.
Hence (8-6) = k√4=k±1
The donkey cannot move at zero speed. i.e. when his speed reduced by 8 kmph. So reduction in speed= 8 kmph
8=1√l=>√l=8 and l=64, when √l=-8, l=64
At 64 kg the donkey will stop.
Solution:
Let quantity of mixture taken from first be x and second be y.
Amount of kerosene oil in the resultant mixture (x+y) is
(7/12)x+(5/8)y=(3/5)(x+y)
(7/12)x-(3/5)x=(3/5)y-(5/8)y-(1/60)x=-(1/40)y=>(x/y)=(6/4)=(3/2)=3:2
Solution:
let the no. of pens in 1st, 2nd and 3rd pencil box be x, 2x and 3x respectively and let the required no. be 3y, 2y and y.
The quantity f pens in the third pencil box would remain the same, hence
3x=y or x =(y/3)
Quantity of pens in the boxes originally is x, 2x and 3x
When x=(y/3), hence quantity is x=(y/3), 2x=(2y/3), 3x=y
i.e (y/3), (2y/3), y
The required number of pens is 3y, 2y and y in
Increase in 1st box=3y-(y/3)=(8/3)y&
Increase in 2nd box = 2y-(2y/3)=(4/3)y
Ratio of increase = (8y/3)L4/3)y=2:1
Solution:
Method-1: Let the total mixture in vessel 1,2 and 3 be 5 litres and 3 litres respectively. So, quantity of water in (5+4+3)=12 litres of mixture is
=(3/5)×5+(4/9) ×4+(3/4) ×3
=3+(16/9)+(9/4)=[(108+64+81)/36]=(253/36)
Quantity of sugar syrup is
12-(253/36)=(179/36)
Ratio of sugar syrup to water = 179:253