CTET Maths - Time and Work
- Option : A
- Explanation : Let n1 and n2 be the speeds in km/hr and let nj be
the greater speed i.e., n1 > n2
⇒ n1 - n2 = 4
⇒ n1 = 4 + n2
⇒ n2(4 + n2)= 120 x 4
⇒ n22 + 4n2 - 480 = 0
⇒ n2 = 20 or -24 (rejected)
∴ n1 = 4 + n2 = 24km/hr
Hence speeds are 24 km/hr and 20 km/hr
Alternatively
Options may also be substituted to find the result.
- Option : C
- Explanation :
Ratio of wages = (3 x 20) : (2 x 30) : (1 x 36) = 5: 5: 3 Total wages of 20 men = 5/13 =Rs.300 ∴ Wages of a man = Rs.15. Similarly, wages of 30 women (5/30) x 780 = Rs.300 Wages of a woman = Rs.10 and wages of 36 children (3/13) x 780 = Rs.180 Wages of a child = Rs.5 ∴ Total wages of 15 men, 21 women and 30 children = 15 x 15 + 21 x 10 + 30 x 5 = Rs.585 ∴ Total wages for 2 weeks = Rs.1170.Men Women Children Work 3 2 1 Numbers 20 30 36
- Option : D
- Explanation : Work done by A in 3 days = 3 x (1/6) = 1/2 of the work
Work done by B in 3 days = 3 x (1/8) = 3/8 of the work
∴ Work done by the boy in 3 days
= Rs. 25
hrs?
- A
If A started the work on the first day followed by B and c, then the work will be finished on the 10th day.
- B
If B started the work on the first day followed by C and A, then the work will be finished on the 11th day.
- C
If C started the work on the first day followed by A and B, then the work will be finished on the 11th day.
- D
None of these
- Option : C
- Explanation : I. Work done by A, Band C together in 3 days
work is
left of which A will finish 6/48 th of work on
10th day and B will finish remaining work on 11th day.
Thus, I is false
II. Work done by A, B, C together in 9 days = 39/48
Work left = 1 - (39/48) = 9/48 th of the whole.
On the 10th day B will finish 1/12 th of the whole.
∴ work left = (9/48) - (1/12) = 5/48 th of the whole.
On 11th day C will finish 1/16 th of the work
∴ work left = (5/48) - (1/16) = 2/48 th of the whole
which will be done by A on the 12th day.
Thus, work will be finished on the 12th day.
Thus, II is false.
III. Work done by A, Band C in 9 days = 39/48
Work left after 9 days = 1 - (39/48) = 9/48 th of the whole
On the tenth day 1/16 th will be finished by C.
∴ work left = (9/48) - (1/16) = 6/48 th of the whole,
which will be finished by A on the eleventh
day. Thus, III is true.
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