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Ten years ago, A’s age was half that of B. If the ratio of the present ages of A and B is 3 : 5, find the total of their present ages.
Let the present ages of A and B are 3x and 5x.
Then, 10 yrs ago, (3x-10) = ½ * (5x-10)
Solve, x = 10
So present ages of A and B are 30 and 50 resp, their sum = 80
3 children A, B and C play a game. A puts Rs 50 and B puts Rs 45. At the end of 4 months, A withdraw half his capital and at the end of 6 months B also withdraws half of his capital. C then enters with a capital of Rs 70. At the end of a year, in what ratio the pofit will be divided?
A’s share : B’s share : C’s share
50*4 + 50/2 * 8 : 45*6 + 45/2 * 6 : 70*6
80 : 81 : 84
13 shirts costs Rs 50 each, 15 pants Rs 60 each, and 12 ties costs Rs 65 each. What is the average value of each article?
Average = 13*50 + 15*60 + 12*65 / 13+15+12=58.25
A sum of Rs 2600 is lent in two parts such that the interest on one part at 10% for 5 years is equal to that on another part at 9% for 6 years. Find the difference in two sums.
Interests are equal. So,
1st part *5*10/100 = 2nd part * 6*9/100
[1st part/2nd part={6*9/100}/{5*10/100}
This gives, 1st part : 2nd part = 27 : 25
So 1st part = 27(27+25) * 2600 = 1350
2nd part = 2600 – 1350 = 1250
So diff = Rs 100
A vessel contains milk and water with a total quantity of 80 litres. 70% of milk and 30% of water is taken out of the vessel. It is found that the vessel is vacated by 55%. What is the initial quantity of milk and water respectively (in litres)?
By method of allegation:
Milk water
70% 30%
. 55%
25% 15%
25 : 15 = 5 : 3
Milk = 5/(5+3) * 80 = 50 l
Water = 80 – 50 = 30 l
5 men can prepare 10 toys in 6 days working 6 hrs a day. Then how many toys will be prepared by 12 men in 3 days working 8 hrs a day?
Here making toys is a work. So,
M1D1T1W2 = M2D2T2W1
This gives, 5×6×6× W2 = 12×3×8×10
W2 = 16 toys
A bag contains 3 white balls, 5 black balls and 4 yellow balls. 2 balls are drawn at random. What is the probability that both the balls are black in color?
From 5 black balls, ways for 2 balls is 5C2 = 5*4/2*1 = 10
There are a total of 12 balls. Ways for drawing 2 balls is 12C2 = 12*11/2*1 = 66
So required prob. = 5C2 / 12C2 = 10/66 = 5/33
An article costs Rs 480. A part of it is sold at 20% loss and the remaining part at x% profit thereby making a total of 5% profit on the whole transaction. Ratio of parts sold at x% profit and 20% loss is 5 : 1. Find the value of x.
By the method of allegation:
Loss profit
-20 x
. 5
x-5 5-(-20)=25
Ratio at 20% loss to x% profit = 1 : 5
So x-5/25 = 1/5
Solve, x = 10
A person travels from A to B at 60 km/hr and back from B to A at 40 km/hr. if eth total time taken for the journey is 30 minutes, find the total distance travelled by the man?
When we are given total time for 2 journeys of equal distance,
One way distance = multiplication of speeds/addition of speeds * total time
So here distance from A to B = 60*40/(60+40) * 30/60 = 12 km
30 min is converted to hrs
30 min 12km
so.60 min ?
So total distance travelled = 2*12 = 24
Let the present ages of A and B are 3x and 5x.
Then, 10 yrs ago, (3x-10) = ½ * (5x-10)
Solve, x = 10
So present ages of A and B are 30 and 50 resp, their sum = 80
3 children A, B and C play a game. A puts Rs 50 and B puts Rs 45. At the end of 4 months, A withdraw half his capital and at the end of 6 months B also withdraws half of his capital. C then enters with a capital of Rs 70. At the end of a year, in what ratio the pofit will be divided?
A’s share : B’s share : C’s share
50*4 + 50/2 * 8 : 45*6 + 45/2 * 6 : 70*6
80 : 81 : 84
13 shirts costs Rs 50 each, 15 pants Rs 60 each, and 12 ties costs Rs 65 each. What is the average value of each article?
Average = 13*50 + 15*60 + 12*65 / 13+15+12=58.25
A sum of Rs 2600 is lent in two parts such that the interest on one part at 10% for 5 years is equal to that on another part at 9% for 6 years. Find the difference in two sums.
Interests are equal. So,
1st part *5*10/100 = 2nd part * 6*9/100
[1st part/2nd part={6*9/100}/{5*10/100}
This gives, 1st part : 2nd part = 27 : 25
So 1st part = 27(27+25) * 2600 = 1350
2nd part = 2600 – 1350 = 1250
So diff = Rs 100
A vessel contains milk and water with a total quantity of 80 litres. 70% of milk and 30% of water is taken out of the vessel. It is found that the vessel is vacated by 55%. What is the initial quantity of milk and water respectively (in litres)?
By method of allegation:
Milk water
70% 30%
. 55%
25% 15%
25 : 15 = 5 : 3
Milk = 5/(5+3) * 80 = 50 l
Water = 80 – 50 = 30 l
5 men can prepare 10 toys in 6 days working 6 hrs a day. Then how many toys will be prepared by 12 men in 3 days working 8 hrs a day?
Here making toys is a work. So,
M1D1T1W2 = M2D2T2W1
This gives, 5×6×6× W2 = 12×3×8×10
W2 = 16 toys
A bag contains 3 white balls, 5 black balls and 4 yellow balls. 2 balls are drawn at random. What is the probability that both the balls are black in color?
From 5 black balls, ways for 2 balls is 5C2 = 5*4/2*1 = 10
There are a total of 12 balls. Ways for drawing 2 balls is 12C2 = 12*11/2*1 = 66
So required prob. = 5C2 / 12C2 = 10/66 = 5/33
An article costs Rs 480. A part of it is sold at 20% loss and the remaining part at x% profit thereby making a total of 5% profit on the whole transaction. Ratio of parts sold at x% profit and 20% loss is 5 : 1. Find the value of x.
By the method of allegation:
Loss profit
-20 x
. 5
x-5 5-(-20)=25
Ratio at 20% loss to x% profit = 1 : 5
So x-5/25 = 1/5
Solve, x = 10
A person travels from A to B at 60 km/hr and back from B to A at 40 km/hr. if eth total time taken for the journey is 30 minutes, find the total distance travelled by the man?
When we are given total time for 2 journeys of equal distance,
One way distance = multiplication of speeds/addition of speeds * total time
So here distance from A to B = 60*40/(60+40) * 30/60 = 12 km
30 min is converted to hrs
30 min 12km
so.60 min ?
So total distance travelled = 2*12 = 24
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