Math Quiz - 1 - Quiz & Trivia

1. In how much time will a train,which is 150 m long and travelling at 90 kmph, cross a platform 100 m long?

5 seconds

15 seconds

12 seconds

10 seconds

Distance to be covered = 150+100 = 250 m
Speed of the train = 90 kmph = 90x(5/18) m/sec = 25 m/sec.
Time taken for the train to cross the platform = 250/25 = 10 seconds.

Explanation

Distance to be covered = 150+100 = 250 m
Speed of the train = 90 kmph = 90x(5/18) m/sec = 25 m/sec.
Time taken for the train to cross the platform = 250/25 = 10 seconds.

2. The ratio of girls to boys in a class of 60 students is 2:3. If the average age of the girls is 17 years while the average age of the boys is 19 years, find the average age of the students in the class?

17.5

17.8

18.5

18.2

During the night the high contrast between the bright moon and the night's dark skies make theAccording to the problem,
Average age of the class = (2x17+3x19) /5
= (57+34)/5 = 91/5 = 18.2

Explanation

During the night the high contrast between the bright moon and the night's dark skies make theAccording to the problem,
Average age of the class = (2x17+3x19) /5
= (57+34)/5 = 91/5 = 18.2

3. If x:y = 2:3, y:z = 4:5 and z is 15 more than y, find the value of x.

20

30

40

50

y:z = 4:5 and z is 15 more than y.
So, y will be 60 and z will be 75.
Now, x:y = 2:3 and so if y is 60, x will be 40.

Explanation

y:z = 4:5 and z is 15 more than y.
So, y will be 60 and z will be 75.
Now, x:y = 2:3 and so if y is 60, x will be 40.

4. X and Y can do a work in 12 days while Y and Z can do it in 20 days. If Y can do the work alonein 30 days, in how many days can X, Y and Z do the work together?

10 days

15 days

8 days

12 days

Let the total work be 60 Units
X and Y : 12 days 5 units/day
Y and Z : 20 days 3 units/day
Y alone : 30 days 2 units/day
Using the above 3 relations,
X alone can do 5-2 = 3 units per day
Z alone can do 3-2 = 1 unit per day.
X,Y and Z together can do 2+3+1 = 6 units per day. Therefore, together they can do the work in 10 days.

Explanation

Let the total work be 60 Units
X and Y : 12 days 5 units/day
Y and Z : 20 days 3 units/day
Y alone : 30 days 2 units/day
Using the above 3 relations,
X alone can do 5-2 = 3 units per day
Z alone can do 3-2 = 1 unit per day.
X,Y and Z together can do 2+3+1 = 6 units per day. Therefore, together they can do the work in 10 days.

5. If the value of A is 20% more than B, then by what percentage is 50% of B more or less than ¾ of A?

25%

50%

33.33%

44.44%

Moon is round because of formed and collapsed under the force of their own grLet B be 100. Then A is 120.
50% of B = 50
¾ of A = 90
Hence, 50% of B less than ¾ of A by 40.
Percentage: (40/90) x 100 = 44.44%

Explanation

Moon is round because of formed and collapsed under the force of their own grLet B be 100. Then A is 120.
50% of B = 50
¾ of A = 90
Hence, 50% of B less than ¾ of A by 40.
Percentage: (40/90) x 100 = 44.44%

6. Find the day of the week on 1st January 2010.

Wednesday

Thursday

Friday

Saturday

We will have to calculate from 1st January AD.
2000 years = 0 odd days.
Next 9 years will have:
2 leap years = 4 odd days and
7 ordinary years = 7 odd days
We need to include 1st January = 1 odd day.
Total number of odd days = 4 + 7 + 1 odd days = 12 odd days = 5 odd days.
Hence, 1st January 2010 will be a Friday.

Explanation

We will have to calculate from 1st January AD.
2000 years = 0 odd days.
Next 9 years will have:
2 leap years = 4 odd days and
7 ordinary years = 7 odd days
We need to include 1st January = 1 odd day.
Total number of odd days = 4 + 7 + 1 odd days = 12 odd days = 5 odd days.
Hence, 1st January 2010 will be a Friday.

7. The present age of a mother and son is in the ratio 8:1. The difference in their ages after 3 yearswill be 4 times the age of the son. Find the ratio of their ages 3 years ago?

28:1

29:1

8:2

7:2

Let their present age be 8x and x respectively.
After 3 years, their age will be 8x+3 and x+3 respectively.
Difference in their age = 7x.
According to the problem 7x=4(x+3)
7x=4x+12
3x=12 or, x=4
Their present age will be 32 and 4 respectively.
3 years ago, their age would have been 29 and 1 respectively.
Required ratio will be 29:1.

Explanation

Let their present age be 8x and x respectively.
After 3 years, their age will be 8x+3 and x+3 respectively.
Difference in their age = 7x.
According to the problem 7x=4(x+3)
7x=4x+12
3x=12 or, x=4
Their present age will be 32 and 4 respectively.
3 years ago, their age would have been 29 and 1 respectively.
Required ratio will be 29:1.

8. Find the last digit of the number (768)^(abc16)?

6

4

2

Cannot be determined

abc16 will give a remainder of 0 when divided by 4 and so the required last digit will be same as the
last digit of 8^4 = ie the last digit will be 6.

Explanation

abc16 will give a remainder of 0 when divided by 4 and so the required last digit will be same as the
last digit of 8^4 = ie the last digit will be 6.

9. The selling price of 5 items is same as the cost price of 6 items. If the percentage mark-up is 10%, find the overall profit percentage?

20%

30%

32%

41%

It is given that CP of 6 items = SP of 5 items
Let the CP of one item be Rs. 5, then according to the given condition, SP of one item will be Rs. 6. Also, there is a 10% mark-up, which makes the SP (6+10% of 6) = 6.6. Now, Profit= (Rs. 6.6 - Rs.5)= Rs. 1.6.
Profit % = (1.6/5)x100% = 32%.

Explanation

It is given that CP of 6 items = SP of 5 items
Let the CP of one item be Rs. 5, then according to the given condition, SP of one item will be Rs. 6. Also, there is a 10% mark-up, which makes the SP (6+10% of 6) = 6.6. Now, Profit= (Rs. 6.6 - Rs.5)= Rs. 1.6.
Profit % = (1.6/5)x100% = 32%.

10. 3 boys and 3 girls are to be arranged in a straight line. In how many ways can this be done so that no 2 boys are together?

3! x 4!

3! x 3! x 2

3! x 2!

None of these

The question says that no two boys are together. There is no restriction on two girls being together if possible.
The girls can be arranged in 3! ways.
_G_G_G_
Once the girls are seated(marked by G), there are 4 places(marked by underscore_) that the boys can occupy and they can do so in 4C3 x 3! ways = 4! ways.
Total number of ways = 3! x 4! ways.

Explanation

The question says that no two boys are together. There is no restriction on two girls being together if possible.
The girls can be arranged in 3! ways.
_G_G_G_
Once the girls are seated(marked by G), there are 4 places(marked by underscore_) that the boys can occupy and they can do so in 4C3 x 3! ways = 4! ways.
Total number of ways = 3! x 4! ways.

Math Quiz - 1

1. In how much time will a train,which is 150 m long and travelling at 90 kmph, cross a platform 100 m long?

2.

What first name or nickname would you like us to use?

2. The ratio of girls to boys in a class of 60 students is 2:3. If the average age of the girls is 17 years while the average age of the boys is 19 years, find the average age of the students in the class?

3. If x:y = 2:3, y:z = 4:5 and z is 15 more than y, find the value of x.

4. X and Y can do a work in 12 days while Y and Z can do it in 20 days. If Y can do the work alonein 30 days, in how many days can X, Y and Z do the work together?

5. If the value of A is 20% more than B, then by what percentage is 50% of B more or less than ¾ of A?

6. Find the day of the week on 1st January 2010.

7. The present age of a mother and son is in the ratio 8:1. The difference in their ages after 3 yearswill be 4 times the age of the son. Find the ratio of their ages 3 years ago?

8. Find the last digit of the number (768)^(abc16)?

9. The selling price of 5 items is same as the cost price of 6 items. If the percentage mark-up is 10%, find the overall profit percentage?

10. 3 boys and 3 girls are to be arranged in a straight line. In how many ways can this be done so that no 2 boys are together?