Quadratic Equation New Pattern Questions

D.1-5) In the following question two quantities are given Quantity 1 and quantity 2 By solving those quantities give corresponding answer.

Q.41) Quantity 1:Two varieties of wheat are mixed together while the first variety is of 90% pure wheat and the rest contaminants and the other variety having wheat and impurities in the ratio 8:3. Find the proportion of the new mixture thus formed?

Quantity 2:A milkman indulges in adulteration. He mixes water in the milk in the first container. After mixing, the respective ratio between water and milk is 1:7. He pours the mixture in another mixture containing 85% milk in the second container. What is the respective ratio between the milk and water in the second container?

1. a) Quantity 1 ≥ Quantity 2
2. b) Quantity 1 = Quantity 2 (or) No relation
3. c) Quantity 1 > Quantity 2
4. d) Quantity 1 ≤ Quantity 2
5. e) Quantity 1 < Quantity 2

e

Quantity 1:

The ratio of the proportion of first variety=9:1

The ratio of the proportion of second variety=8:3

The new mixture thus formed containing wheat = 9/10+8/11=(99+80)/110=179/110

The new mixture containing impurities = 1/10+3/11=(11+30)/110=41/110

The required ratio=179:41

Quantity 2:

The ratio between the milk and water in the second container before mixing=17:3

The proportion of the milk in second container after mixing = 7/8+17/20=69/40

The proportion of the water in second container after mixing = 1/8+3/20=11/40

The respective ratio between milk and water in the ratio=69:11

179/41<69/11

Comparing the two values, x<y

Q.2) Quantity 1:The speed of a car is two times the speed of a train of length 250m crossing a bridge of 350m in 24 seconds. What is the speed of the car in kmph?

Quantity 2:Two trains of length each 500m cross each other in 12.5 seconds travelling in opposite directions. One of the trains crosses a pole in 10 seconds. What is the speed of the slower train?

1. a) Quantity 1 ≥ Quantity 2
2. b) Quantity 1 = Quantity 2 (or) No relation
3. c) Quantity 1 > Quantity 2
4. d) Quantity 1 ≤ Quantity 2
5. e) Quantity 1 < Quantity 2
c

Quantity 1:

Total length of the train and bridge=250+350=600m

Time taken=24 seconds

Speed of the train = 600/24=25m/s=90 kmph.

So, the speed of the car=180kmph

.Quantity 2:

The speed of the faster train crossing pole = 500/10=50m/s

Let x be the speed of the slower train

=1000/(x+50)=12.5seconds

So, the value of x=30m/s

So, the speed of slower train= 108kmph

Comparing the two values, x>y

Q.3) Quantity 1:Ram invests some amount in scheme A for 3 years at a rate of 5% simple interest. He also invests in scheme B Rs.2000 more than what he invested in scheme A for 2 years at a rate of 6% simple interest. If he gets a total of Rs.1050, then what is the total amount he invested in both the schemes?

Quantity 2:An amount is received by a person at the end of 2 years with a compound interest amount of Rs 615. The interest amount is 10.25% of the principal amount. If the same person receives Rs 768.75 in another scheme for same period and at the same rate, what is his first time investment?

1. a) Quantity 1 ≥ Quantity 2
2. b) Quantity 1 = Quantity 2 (or) No relation
3. c) Quantity 1 > Quantity 2
4. d) Quantity 1 ≤ Quantity 2
5. e) Quantity 1 < Quantity 2
c

Quantity 1:

Let the amount he invested in scheme A be x.

So, the amount he invested in scheme B be x+2000

Now, the equation becomes, (x×3×5)/100+((x+2000)×2×6)/100=1050rs.

X=3000rs.

Total money he invested in both the schemes=8000rs

Quantity 2:

Given that, 615rs is 10.25% of the principal.

So, the principal is 6000rs.

For the second time, he receives 768.75rs as the interest.

So, (x+768.75)=x(1+5/100)²

X=7500

Comparing the two results, x>y

Q.4) Quantity 1:A cube is melted so as to cast several cubes of length of side 2m. The ratio of the length of side of older cube and the newer cube is 3:1 respectively. What is the no of cube so formed?

Quantity 2:

A person jogs around a circular park of diameter 210m. He aimed to cover 6.6kms. How many rounds he has to go to cover the distance?

1. a) Quantity 1 ≥ Quantity 2
2. b) Quantity 1 = Quantity 2 (or) No relation
3. c) Quantity 1 > Quantity 2
4. d) Quantity 1 ≤ Quantity 2
c

Quantity 1:

If the length of one side of newer cube is 2m, then the volume=8m³.

The length of one side of older cube is 6m and its volume would be 216m³.

No of cubes thus formed = 216/8=27

Quantity 2:

The diameter of circular park=210m

The perimeter of the circular park=P=2πr=3.14×2×105=660m.

The no of rounds he has to go for = 6600/660=10

Comparing both the quantities, x>y

1. e) Quantity 1 < Quantity 2

Q.5) Quantity 1:Hari buys a shirt with 4% discount whose marked price is 2100rs. Still the seller gains 12%. What is the cost price of the shirt?

Quantity 2:A seller allows a discount of 10% on a watch. If a customer buys a pair of watch, then he is offered 4% extra discount. He buys two watches for 960rs. What is the price of two couples of watches?

1. a) Quantity 1 ≥ Quantity 2
2. b) Quantity 1 = Quantity 2 (or) No relation
3. c) Quantity 1 > Quantity 2
4. d) Quantity 1 ≤ Quantity 2
5. e) Quantity 1 < Quantity 2
e

Quantity 1:

Hari buys the shirt for = 2100/100×96=2016

The best price is 112% of the cost price.

So, the cost price is, 2106/112×100=1800

Quantity 2:

The marked price of pair of watches = 960/96×100=1000.

The marked price of single watch=500

The cost price of a single watch = 500/90×100=555

The cost price of four watches=555×4=2220

Comparing the two quantities, x<y

D.6-10) In the following question two quantities are given Quantity 1 and quantity 2 By solving those quantities give corresponding answer.

Q.6) Quantity 1:A boy is 4 years older than his brother. After four years from now the boy’s age will be two times his brother’s age after 2 years. What is the ratio of their age 3 years later from now?

Quantity 2:The average age of a family consisting a father, a mother, two boys and the youngest girl child who is 4 years younger than one of her brothers and 2 years younger than another brother is 21. The difference between the ages of mother and father is 5 years. The ratio between the ages of parents and the children is 5:2. What is the ratio between the ages of mother and her girl child if father is the eldest in the family?

1. a) Quantity 1 ≥ Quantity 2
2. b) Quantity 1 = Quantity 2 (or) No relation
3. c) Quantity 1 > Quantity 2
4. d) Quantity 1 ≤ Quantity 2
5. e) Quantity 1 < Quantity 2
e

Quantity 1:

Age of boy=x

Age of his brother=x-4

After 8 years boys age=2×Age of his brother after 4 years

X+4=2×((x-4)+2)

X=8

The required ratio=11:7

Quantity 2:

The sum of the ages of five members=5×21=105

The ratio between parents and children=5:2

So the sum of ages of parents = 105/7×5=75

The sum of the ages of children = 105/7×2=30

The age of mother=35 (since the age of mother is 5 years lesser than father)

Let the age of girl child be x.

The ages of children=x+(x+2)+(x+4)=30

The age of girl child=8

The required ratio=35:8

Comparing both the quantities,  11/7<35/8  i.e X<y

Q.7) Quantity 1:

Which of the following is greater?

4/15,5/17,10/33 and 8/27

Quantity 2:Which of the following is greater?

6/13,7/15,13/19 and 31/50

1. a) Quantity 1 ≥ Quantity 2
2. b) Quantity 1 = Quantity 2 (or) No relation
3. c) Quantity 1 > Quantity 2
4. d) Quantity 1 ≤ Quantity 2
5. e) Quantity 1 < Quantity 2
e

Quantity 1:

0.267, 0.294, 0.303 and 0.296

So, the greatest value is  10/33

Quantity 2:

0.461, 0.467, 0.684 and 0.62

So, the greatest value is  13/19

Comparing the two values ,  10/33<13/19  i.e, x<y

Q.8) Quantity 1:

What is the probability that two cards drawn in random from a deck of cards to be a multiple of 5 or ace?

Quantity 2:A man wants to choose a shirt from his almerah if it contains 2 blue shirts, 3 green shirts, 5 yellow shirts. What is the probability that the shirt is not an yellow shirt?

1. a) Quantity 1 ≥ Quantity 2
2. b) Quantity 1 = Quantity 2 (or) No relation
3. c) Quantity 1 > Quantity 2
4. d) Quantity 1 ≤ Quantity 2
5. e) Quantity 1 < Quantity 2
e

Quantity 1:

Required probability = (8C_2)/(13C_2 )+(4C_2)/(13C_2 )=34/1326=1/39

Quantity 2:

Required probability= (2C_1+3C_1)×1/(10C_1 )=1/2

Comparing both the quantities, x<y

Q.9) Quantity 1:

Two persons A and B started a business in which A invests some money and B invests 4000 more than what A invests. After three months from the start of the business A invested an additional amount which is one fourth of the amount he invested in the beginning. At the end of one year they earn profit in the ratio 57:80. What is the amount invested by the person B?

Quantity 2:P can finish a work in some days where Q takes two times the time taken by P. The efficiency of R is three times the efficiency of P. All the three persons are given a work and the sum of their wages will be Rs 8550. What will be the wage of B?

1. a) Quantity 1 ≥ Quantity 2
2. b) Quantity 1 = Quantity 2 (or) No relation
3. c) Quantity 1 > Quantity 2
4. d) Quantity 1 ≤ Quantity 2
5. e) Quantity 1 < Quantity 2
c

Quantity 1:

From the data given, we can equate,

Solving the above equation, x=Rs.6000.

Quantity 2:

We can take that, the efficiency of P=x

The efficiency of R=3x

The efficiency of Q=x/2

The ratio between the efficiency of P, Q and R= 2:1:6

The wage of Q = 8550/10×1=Rs.855.

Comparing both the quantities,  x>y.

Q.10) Quantity 1: Pipe A can fill a tank in 36 hours while pipe B can fill it in 24 hours. If both the pipes are opened for an hour alternatively starting with A, then in how many hours the pipe will be filled?

Quantity 2:To a cistern, three pipes namely A, B and C are attached. Pipe A can fill the cistern in 12 hours, pipe B can fill the cistern in 15 hours and pipe C can empty the cistern in 20 hours. In how many hours the cistern will be filled?

1. a) Quantity 1 ≥ Quantity 2
2. b) Quantity 1 = Quantity 2 (or) No relation
3. c) Quantity 1 > Quantity 2
4. d) Quantity 1 ≤ Quantity 2
5. e) Quantity 1 < Quantity 2
c

Quantity 1:

Work done by pipe A in one hour = 1/36

Work done by pipe B in one hour = 1/24

Work done by both the pipes in two hours = 1/36+1/24=5/72

Both the pipe will do the work for 28 hours to complete 70/72  of the work.

Remaining 2/72 of the work will be done by A in one hour.

So totally 29 hours will be taken by both the pipes to fill the tank.

Quantity 2:

Work done by pipe A = 1/12

Work done by pipe B = 1/15

Work done by pipe C =- 1/20

Total work done in one hour by all the three pipes = 1/12+1/15-1/20=1/10

The cistern will be filled in 10 hours.

Comparing the two values, x>y