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# Maths Quiz for 2016-17 Exams

1. A is 2  1 ⁄ 3  times as fast as B. If A gives B a start of 80 m, how long should the race course be so that both of them reach at the same time?
A. 170 m
B. 150 m
C. 140 m
D. 160 m
Speed of A : Speed of B =  7 ⁄ 3  : 1 = 7 : 3
It means, in a race of 7 m, A gains (7-3)=4 m
If A needs to gain 80 m, race should be of 74×80 = 140 m

2. A can run 224 metre in 28 seconds and B in 32 seconds. By what distance A beat B?
A. 36 m
B. 24 m
C. 32 m
D. 28 m
Clearly, A beats B by 4 seconds
Now find out how much B will run in these 4 seconds
Speed of B =224/32=7 m/s
Distance covered by B in 4 seconds = Speed × time =7×4=28 m

3. In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:
A. 21 m
B. 28 m
C. 26 m
D. 29 m
When A covers 100 m, B covers (100-25)=75 m
When B covers 100 m, C covers (100-4)=96 m
=When B covers 75 metre, C covers 96100×75=72 m
i.e., When A covers 100 m, B covers 75 m and C covers 72 m
= In a 100 m race, A beat C by (100-72)=28 m

4. A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is:
A. 4.4 kmph
B. 4.25 kmph
C. 4.14 kmph
D. 5.15 kmph
speed of A = 5 kmph = 5×5/18=25/18m/s
Time taken by A to cover 100 m=distance/speed=100/(25/18) = 72 seconds
It is given that, A gives B a start of 8 m and still beats him by 8 seconds.
= B takes (72+8)=80 seconds to cover (100-8)=92 metre
Speed of B =distance/time=92/80m/s=92/80×18/5 kmph = 4.14 kmph

5.In how many different ways can the letters of word‘PREVIOUS’ be arranged in such a way that the vowels always come together?
A. 50400
B. 4840
C. 3260
D. 2880
Total letters are ‘8’ and No of vowels = 4
So total no of ways=5! * 4! = 2880

6. To Finish a work, B will take three times as long as A and C together and C will take twice as long as A and B together. If the three persons A, B and C together can finish the work in 20 days , then how long will A take to finish the work alone?
A. 30 days
B. 45 days
C. 48 days
D. 60 days
3*B’s daily work= (A+C)’s daily work
4*B’s daily work = (A+B+C)’s daily work = 1/20
B’s daily work = 1/80
2*C’s daily work = (A+B)’s daily work
3*C’s daily work = (A+B+C)’s daily work = 1/20
C’s daily work= 1/60
A’s daily work= 1/20 – (1/80 + 1/60) = 1/48
A can finish the work in 48 days.

7.The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:
A. 15360
B. 153600
C. 30720
D. 307200
Perimeter = Distance covered in 8 min. = (12000/60x 8)m = 1600 m.
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m^2

8. At present Ayushi is eight times her daughter’s age. Eight years from now, the ratio of the ages of Ayushi and her daughter will be 10 : 3 respectively. What is Ayushi’s present age ?
A. 32 years
B. 40 years
C. 36 years
D. Can’t say
Let the age of Ayushi’s daughter be x. Then Ayushi’s age is 8x.
(8x + 8)/ (x + 8) = 10/3
x = 4
Ayushi present age = 8x = 32 years.

9. In how many different ways can 4 boys and 3 girls be arranged in a row such that all the boys stand together and all the girls stand together?
A. 75
B. 576
C. 288
D. 24
Required number of ways = 4! * 3! * 2! = 288.

10. A radio is sold for Rs 990 at a profit of 10%. What would have been the gain or loss in percentage had it been sold for Rs 880?
A. 19/3%  gain
B. 17/3% loss
C. 17% gain
D. 20/9% loss
Let the CP is Rs x.
Then, x * 110/100  = 990
x = 900
Now CP is Rs 900 and SP is 880.
% loss =  20/900 * 100 = 20/9%