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Maths Quiz (Time & Work) for KVS/NVS and CTET Exams

Q1. Subhash can copy 50 pages in 10 h, Subhash and Prakash can copy 300 pages in 40 h. how much time can Prakash copy 30 pages?
(a) 12 h
(b) 9 h
(c) 13 h
(d) 10 h

Q2. A takes twice as much as B and thrice as much as C to complete a piece of work. They together complete the work in 1 day. In what time will A alone complete the work?
(a) 9 days
(b) 5 days
(c) 6 days
(d) 4 days

Q3. x number of men can finish a piece of work in 30 days. If there were 6 men more, the work could be finished in 10 days less. The original number of men is
(a) 6
(b) 10
(c) 12
(d) 15

Q4. 42 women can do a piece of work in 18 days. How many women would be required to do the same work in 21 days?
(a) 36
(b) 24
(c) 30
(d) 44

Q5. 3 men can complete a piece of work in 6 days. 5 women can complete the same work in 18 days. In how many days will 4 men and 10 women together complete the same work?
(a) 3 days
(b) 5 days
(c) 2 days
(d) 4 days

Q6. 8 men and 4 women together can complete a piece of work in 6 days. Work done by a man in one day is double the work done by a woman in one day. If 8 men and 4 women started working and after 2 days, 4 men left and 4 new women joined, in how many more days will the work be completed?
(a) 5 days
(b) 8 days
(c) 6 days
(d) 4 days

Q7. 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?
(a) 50
(b) 45
(c) 40
(d) 35

Q8. Ram earns Rs. 125 in 8 days and Shyam earns Rs. 140 in 10 days, the ratio of their earnings is
(a) 125 : 110
(b) 112 : 125
(c) 125 : 112
(d) 100 : 112

Q9. A man and a boy received Rs. 800 as wages for 5 days for the work they did together. The man’s efficiency in the work was three times that of the boy. What are the daily wages of the boy?
(a) Rs. 76
(b) Rs. 56
(c) Rs. 44
(d) Rs. 40

Q10. A, B and C completed a work costing Rs. 1800. A worked for 6 days, B for 4 days and C for 9 days. If their daily wages are in the ratio of 5 : 6 : 4, then how much amount will be received by A?
(a) Rs. 800
(b) Rs. 600
(c) Rs. 900
(d) Rs. 750

Solutions

S1. Ans.(a)
Sol. Given, number of pages copied by Subhash in 10 h = 50 pages
∴ Number of pages copied by Subhash in 1 h =50/10 = 5 pages
Now, number of pages copied by Subhash and Prakash in one hour
=300/40=15/2 pages
Let time taken by Prakash to copy 30 pages = x h
∴ Number of pages copied by Prakash in one hour=30/x
Now, according to the question,
=(30/x)+5=15/2
⇒ 30/x=(15/2)-5=5/2
⇒ 30/x=5/2
⇒ x=(2 × 30)/5=12
⇒ x = 12 h

S2. Ans.(c)
Sol. Let time taken by C to complete the work = x days
Time taken by A to complete the work = 3x days
Time taken by B to complete the work =3x/2 days
According to the question,
(1/3x)+1/(3x/2)+1/x=1
⇒ (1/3x)+(2/3x)+(1/x)=1
⇒ (1 + 2 + 3)/3x=1
⇒ 6/3x=1
⇒ 2/x=1
⇒ x = 2
∴ Time taken by A = 3x = 3 × 2 = 6 days

S3. Ans.(c)
Sol. M1 D1 = M2 D2
x × 30=(x+6)×20
3x = 2x + 12
x = 12
So, the number of men is 12.

S4. Ans.(a)
Sol. Since, 42 women can complete the work in 18 days
So, 1 women can complete the work in 42 × 18 days
Number of women required to complete the same work in 21 days
=(42×18)/21 = 36 women

S5. Ans.(a)
Sol. 18 men = 5 × 18 = 90 women
⇒ 1 man = 5 women
⇒ 4 men + 10 women = 30 women
⇒ M1 D1 = M2 D2
⇒ 5×18 = 30 × D2
⇒ D2=(5 × 18)/30 = 3 days

S6. Ans.(a)
Sol. 1 male = 2 females
8 males and 4 females = 20 females
After 2 days, 4 males have left the work
and 4 females joined at their place
= 4 males + 8 females
= 8 + 8 females
= 16 females
Here, M1= 20 females
D1=6-2 = 4 days
M2= 16 females, D2= ?
∴ M1 D1 = M2 D2
20×4=16×D2
⇒ D2=(20 × 4)/16
⇒ D2= 5 days

S7. Ans.(c)
Sol. Let 1 man’s 1 day’s work = x
And 1 woman’s 1 day’s work = y
Then, 4x+6x=1/8 …(i)
And 3x+7y=1/10 …(ii)
On solving equation (i) and (ii), we get
y=1/400
1 woman’s 1 day’s work =1/400
∴ 10 women’s 1 day’s work
=10/400=1/40
Hence, 10 women will finish the work in 40 days.

S8. Ans.(c)
Sol. Since, earnings of Ram and Shyam
Rs. 125/8 and Rs. 140/10 per day
∴ Required ratio =(125/8):(140/10)
= (125 × 10) : (140 × 8)
= 125 : 112

S9. Ans.(d)
Sol. Total money = Rs. 800
According to the question,
Man : Boy = 3 : 1
∴ Boy’s share =(1/4) × 800 = Rs. 200
∴ The daily wages of boy
= Rs.(200/5) = Rs.40

S10. Ans.(b)
Sol. Total money = Rs. 1800
Ratio of wages of A, B and C respectively
= 5 × 6 : 6 × 4 : 4 × 9
= 30 : 24 : 36
= 5 : 4 : 6