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Maths Quiz for KVS and NVS Exams 2016

1. 3 persons undertake to complete a piece of work for Rs. 1,200. The first person can complete the work in 8 days, second person in 12 days and third person in 16 days. They complete the work with the help of a fourth person in 3 days. What does the fourth person get?
(a) Rs. 180
(b) Rs. 200
(c) Rs. 225
(d) Rs. 250
Sol.
Let the fourth person complete the entire work in x days.
Now, according to the question:
3/8+3/12+3/16+3/x=1
⇒1/x=1/3-1/8-1/12-1/16=(16 – 6 – 4 – 3)/48=1/16
∴ x = 16
Ratio of wages =1/8 ∶1/12 ∶1/16 ∶1/16=6∶4∶3∶3
Sum of ratios = 6 + 4 + 3 + 3
∴ Fourth person’s share =3/16×1200  =Rs. 225.

2. A can do a piece of work in 20 days and B in 30 days. They work together for 7 days and then both leave the work. Then C alone finishes the remaining work in 10 days. In how many will C finish the full work?
(a) 25 days
(b) 30 days
(c) 24 days
(d) 20 days
Sol.
Work done by A and B in 7 days
=7/20+7/30=(21+14)/60=35/60=7/12
Remaining work =1-7/12=5/12
∴ Time taken by C =12/5×10= 24 days

3. A does 1/5 of a work in a week. B finishes the work in 15 Days. B starts the work and works only for 3 days. Thereafter A completes the job. He will finish it in:
(a) 10 days
(b) 7 days
(c) 12 days
(d) 28 days
Sol.
Time taken by A in doing the work = 35 days
Time taken by B in doing the same work = 15 days
B’s 3 days’ work =3/15=1/5
Remaining work =1-1/5=4/5
∴ Time taken by A in finishing the remaining work =(35×4/5)=28  days

4. 2 men and 4 boys can do a piece of work in 10 days, while 4 men and 5 boys can do it in 6 days. Men and boys are paid wages according to their output. If the daily wage of a man is Rs. 40, then the ratio of daily wages of a man and a boy will be:
(a) 5 : 3
(b) 5 : 2
(c) 7 : 4
(d) 7 : 3
Sol.
(2m+4b)×10=(4m+5b)×6
⇒20m+40b=24m+30b
⇒4m=10b
⇒2m=5b
∴5b=2×40
⇒b=(2×40)/5=16
∴ required ratio = 40 : 16 = 5 : 2

5. P, Q, R are employed to do a work for Rs. 5750. P and Q together finished 19/23 of work and Q and R together finished 8/23 of work. Wage of Q in rupees, is:
(a) 2850
(b) 3750
(c) 2750
(d) 1000
Sol.
Work done by (P + Q + R) = 1  …(i)
Work done by (P + Q) =19/23               …(ii)
Work done by (Q + R) =8/23       …(iii)
From equations (ii) + (iii) – (i)
Q =19/23+8/23-1=(27 –  23)/23=4/23
∴ Wages of Q =4/23×5750 = Rs. 1000

6. X can do a piece of work in 20 days and Y can do it in 10 days. They started together, but after 6 days X leaves off. Y will do the rest work in
(a)  1 day
(b)  2 days
(c)  7/3 days
(d)  3 days
Sol.
(X + Y)’s 6 days’ work = 6 * (1/20 + 1/10) = 9/10
Remaining work = 1 – 9/10 = 1/10
1/10 work is done by Y in 10 * 1/10 = 1 day

7.The average wage of 500 workers was found to be Rs. 200. Later on it was discovered that the wages of two workers were misread as 180 and 20 instead of 80 and 220. The correct average wage is :
(a) Rs. 200.10
(b) Rs. 200.20
(c) Rs. 200. 50
(d) Rs. 201.00
Sol.
Total wages of 500 workers
= 500 * 200 = 100000
Now, according to question,
= (100000 – 180 – 20 + 80 + 220)/500
= 100100/500 = Rs. 200.20

8. A bag contains Rs 216 in the form of one rupee, 50 paise and 25 paise coins in the ratio of 2 : 3 : 4. The number of 50 paise coins is:
(a) 96
(b) 144
(c) 114
(d) 141
Sol.
Let number of one-rupee coins = 2 K
Number of 50-paise coins = 3 K
Number of 25-paise coins = 4 K
2K × Rs. 1 + 3 K × Rs. 0.5 + 4K × Rs. 0.25 = Rs. 216
⇒ 2 K + 1.5K + K = 216
K=48
The number of 50 paise coins=3K=144

9. Three years ago the average age of a family of 5 members was 17 years. With the birth of a new baby, the average remains the same even today. Find out the age of the baby.
(a) 1 year
(b) 3 years
(c) 2.5 years
(d) 2 years
Sol.
Present age of 5 members
= (5 × 17 + 3 × 5) years.
= 100 years
Present age of 5 members and a baby
= 17 × 6 = 102 years.
∴ Age of the baby = (102 – 100) years.
= 2 years.

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
Sol.
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% Join India's largest learning destination

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