APTITUDE MIX

PERCENTAGE

The total number of  girls in a class is 45% more than the total number of boys in the class.The total number of students in the class is 294 then what is the difference between the total number of girls and boys ?

No of boys = x         No of girls =X + x(45/100)     = 29x/20
Total = X+(29x/20) = 294
49x = 294×20 = 5880
X = 5880/49 = 120(boys)
Girls = (29×120)/20 = 174
Difference = 174 – 120 = 54

Mil contain 10% of  water.What quantity of pure milk is should be added to 15litre of milk to reduce the water percentage is 7%

10% of water in 15 lit of milk =(10/100) × 15 = 1.5
X lit of pure milk added to reduce water to 7% 

150  =  105+7x
7x   = 45
X  = 45/7 = 6.4lit

The price of sugar is  reduced by 3%.How many kg of sugar can now be bought for the money which was sufficient to buy 50kg of rice earlier ?

Let one kg of sugar earlier = Rs. 100
50 kg of sugar earlier = Rs. 5000
Now 1 kg of sugar = Rs.97
Quantity to buy now = 5000/97 = 51.5kg

Sugar contain 5% water .What quantity of pure Sugar should be added to 10 litres of water to reduce this to 2%.

0.5/(x+10)=2/100.
2x=30
X=15.

Raj save 10%,after 2 years when his income is increased by 10%,he could save the same money then how much his expenditure increased?

Let income=100,saving=10 and expenditure=90.
New income=110,saving=11 and e=99.
E increased %=[(99-90)/90] ×100=(9/90)×100=10%

TIME DISTANCE AND SPEED

Two trains approach each other at 20kmph and 24kmph from 2 places 240km apart. After how many hours they will meet ?

Explanation :
20x + 24x = 240
44x = 240
X = 240/44 = 5.45hrs

A business man travelled 120km by bus ,Which formed 2/5 of his trip.He travelled 1/3 of the whole trip by car and the rest by train.The distance travelled by train is

2/5 x = 120km
Total distance = x(5×120)/2 = 300km
Remaining trip = 300 – 120 = 180
Distance travelled by car = 300/3 = 100km
Distance travelled by train = 180 – 100 = 80km

A train Express A leaves Delhi at 5 a.m and reaches Mumbai at 9 a.m.Another train Express B leaves Mumbai at 7 a.m and reaches Delhi at 10.30 a.m.At what time do they cross each other ?

Speed of Express A = x/4kmph
Speed of Express B = 2x/7kmph =>(t=3.30 = 3(1/2) = 7/2)
Trains will meet T hours after 7 a.m
(x/4)(y+2) + (2x/7)y = x
(y+2)/4 + (2y/7) = 1
(7y+14+8y)/28 = 1
15y = 28-14
Y =(14/15)×60 = 56 min

A Bus covers a distance of 36km at a uniform speed.Had the speed been 6 kmps less, it would have taken one hour more for the journey.The original speed of the bus is

 

X^2 – 6x – 216 = 0
x^2-18x+12x-216 = 0
(x+12)(x-18) = 0
X = 18kmph

A man can reach a certain place in  30hrs.If he reduces his speed by 1/10 th, he goes 9km less in that time. Find his speed ?

Let x be the distance
30x – 27x = 9      3x = 9
X= 3 kmph

Rahul started his journey on bike at 7.30pm at a speed of 8km/ph. After 30m, Lenin started his journey from the same place with the speed of 10km/ph. At what time did Lenin overtake Rahul ?

RAHUL 1HOUR =8KM/HR                SO        ½ HOUR=4KM/HR

LENIN 1HOUR=10KM/HR                SO        ½ HOUR=5KM /HR

RAHUL       8.00                 8.30             9.00             9.30             10.00

                4KM                 8KM              12KM            16KM            20KM

LENIN        8.00                 8.30             9.00             9.30             10.00  

                0KM                 5KM              10KM            15KM            20KM

A bus reached Mumbai from Hyderabad in 30min with an average speed of 50kmph. If the average speed is increased by 35kmph ,How long will it take to cover the same distance ?

Time = [ 50 × (30/60) ] / (50 +35)
= [150/60] / 85
= 17.6 / 60 hr = 17.6 min = 18min

Speed of a boat in standing water is 9kmph and the speed of the
stream is 1.5kmph. A man rows to a place at a distance of 10.5 km and
comes back to the starting point. Find the total time taken by him.

Speed in still water= ½ (a+b) = 9km ph
= a+b = 18 …………….1
speed of the stream = ½ (a-b) = 1.5 kmph
= a-b = 3 kmph…………2
solving 1 and 2 gives a = 10.5km/hr ; b=7.5 kmphr
Total time taken by him = 105/10.5 + 105/7.5 = 24 hours

A man rows to a place 48km distant and back in 14 hours. He finds
that he can row 4km with the stream in the same time as 3km against the
stream. Find the rate of the stream.

Suppose he moves 4km downstream in x hours
Then, downstream a= 4 / x km/hr
Speed upstream b = 3/ x km/hr
48 / 4 /x + 48 / 3/x = 14
x/4 + x/3 = 14/48 = 1/4
3x + 4x / 12 = 1/4
7x x 4 = 12 so,x = 3/7
a=28/3 km/hr ,b = 7km/hr
rate of stream = ½ (28/3 – 7 )
= 7/6 = 1.1 km/hr

A train travelling at a speed of 75 mph enters a tunnel 7/2 miles long. The train is 1/4 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?

Actually train is covering length of tunnel + its own length here
so total distance = 7/2 + 1/4= 15/4 miles
time= distance /speed
time= (15/4) / 75 = 1/20 hour
(1/20)x60 = 3 min

Ratio & Proportion

The ratio of prices of 2 dresses is 10:15.If the price of the first dress is increased by 10% and that of the second dress by Rs.400 then the ratio of their prices is 4:7.What are the initial prices of the dresses ?

Let the initial price of the dress = 10x and 15x
Price of the 1^st dress after increment = 10x × (110/100) = 11x
Price of the ^2nd dress after increment = 15x+400
[11x/(15x+400)] = 4/7
77x = 60x + 1600
17x = 1600
X = 1600/17 = 94.11 = 94

Raju,Vikram and Rihan are invested some amount into the business.Vikram invested double the amount after 6 mionths and Rihan invested thrice the amount invested by Raju after 8 months.What is  Rihan’s share in profit if they earn a profit of Rs.60000 at the end of 1 year ?

Investment Ra = X for 12 months = 12x
Investment V = 2X for 6 months = 12x
Investment Ri = 3X for 4months = 12x
Raju : Vikram : Rihan = 12:12:12 = 1:1:1
Rihan’s share in profit = 1/3×60,000 =20,000

Sunny’s monthly income is 60% of Anu’s. The ratio of Sujy’s monthly income to Anu’s is 8:11. And their (Sujy and Anu’s) average monthly income is Rs.43700. What is Sunny’s monthly income?

Anu’s monthly income (11/19) × 43700 × 2 = Rs. 50600
Sunny’s Monthly Income = 56000 × (60 /100) = 30360

Raju bought 10 honey bottles of equal size. If He sells his honey at Rs.50 per a kg, he losses Rs.200.While selling it at RS.60per kg he gains Rs. 150 on the whole. Find the amount of honey in each bottle?

Suppose he has x kg of honey.
Thus we have 50x + 200 = 60x – 150 (Equating CP in both cases)
=> x= 35 kg           Each bottle contains (35/ 10) = 3.5 kg

CONCEPT

Suppose he has x kg of honey.
50*X =50X AND 60*X=60X   NOW

SP=50X AND LOSS=200……….LOSS=CP-SP………CP=-SP-LOSS…….CP=-50X-200-----à(1)

SP=60X AND GAIN=150………GAIN=SP-CP……….-CP=SP-GAIN…CP=-SP+GAIN..

                                                                                      CP=-60X+150------à(2)

-50X-200=-60X+150………..-50X+60X=150+200……10X=350……X=35

Each bottle contains (35/ 10) = 3.5 kg

Mr.Rawat leaves for a place B at morning 6 am from place A and reaches there at 10 am. Mr. Basu leaves from place B at 8 am and reaches Place A at 12 pm. When they both will meet each other?

Let the ditance between A & B =x km and they meet each other after y hrs after Mr.Rawat started his journey.
Avg Speed of Mr.Rawat= x/(10am-6am)= (x/4) km/hr
Similarly for Mr.Basu ,Avg Speed = x/(12pm-8am)= (x/4) km/hr
Distance travelled by Mr. Rawat = (xy/4) km
and Distance travelled by Mr. Basu= x(y-2)/4 km [ as Mr. basu started 2 hrs after Mr. Rawat] Now (xy/4) + x(y-2)/4 =x
=> y = 3 hrs
So they will meet 3 hrs after Mr. Rawat started his journey = 6 am+ 3 hrs =9am

A Wholesale dealer claims lending money to its vendor at Simple Interest, but it includes the interest every 6 months for calculating the principal. If he charges 12% interest the effective rate of interest becomes:

Let the Principal =Rs.100
Then SI for 6 months= (100 × 12 ×1)/(100 × 2)= Rs.6
SI for last 6mnths= (106 × 12 × 1)/(100 × 2)= Rs.6.36
So the amount at the end of the year =100+6+6.36 =112.36
Thus effective rate= 112.36-100 =12.36%