Mathematics Mcqs

The edges of a cuboid are in the ratio 1 : 2 : 3 and its sunface area is 88 cm2. The volume of the cuboid is :_________?

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The edges of a cuboid are in the ratio 1 : 2 : 3 and its sunface area is 88 cm2. The volume of the cuboid is :_________?

A. 24 cm3
B. 48 cm3
C. 64 cm3
D. 120 cm3
Let the dimensions of the cuboid be x, 2x and 3x.
Then, 2 (x X 2x + 2x X 3x + x X 3x) = 88
⇔ 2X2 6X2 + 3X2 = 44 ⇔ 11X2 = 44 ⇔ X2 = 4 ⇔ x = 2.
Volume of the Cuboid = (2 X 4 X 6) cm3 = 48 cm3.

A cuboidal, block of 6 cm X 9 cm X 12 cm is cut up into an exact number of equal cubes. The least possible number of cubes will be_________?

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A cuboidal, block of 6 cm X 9 cm X 12 cm is cut up into an exact number of equal cubes. The least possible number of cubes will be_________?

A. 6
B. 9
C. 24
D. 30
Volume of block = (6 X 9 X 12) cm3 = 648 cm3.
Side of largest cube = H.C.F. of 6 cm, 9 cm, 12 cm = 3 cm.
Volume of this cube = (3 X 3 X 3) = 27 cm3.
Number of cubes = 648/27 = 24.

P and Q can complete a work in 15 days and 10 days respectively. They started the work together and then Q left after 2 days. P alone completed the remaining work. The work was finished in__________days.

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P and Q can complete a work in 15 days and 10 days respectively. They started the work together and then Q left after 2 days. P alone completed the remaining work. The work was finished in__________days.

A. 12
B. 15
C. 22
D. 20
Work done by P in 1 day = 1/15
Work done by Q in 1 day = 1/10
Work done by P and Q in 1 day = 1/15 + 1/10 = 1/6
Work done by P and Q in 2 days = 2 × (1/6) = 1/3
Remaining work = 1 – 1/3 = 2/3
Time taken by P to complete the remaining work 2/3 = (2/3) / (1/15) = 10 days
Total time taken = 2 + 10 = 12 days

A and B can finish a work 30 days if they work together. They worked together for 20 days and then B left. A finished the remaining work in another 20 days. In how many days A alone can finish the work?

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A and B can finish a work 30 days if they work together. They worked together for 20 days and then B left. A finished the remaining work in another 20 days. In how many days A alone can finish the work?

A. 70
B. 50
C. 40
D. 60
Amount of work done by A and B in 1 day = 1/30
Amount of work done by A and B in 20 days = 20 × (1/30) = 20/30 = 2/3
Remaining work – 1 – 2/3 = 1/3
A completes 1/3 work in 20 days
Amount of work A can do in 1 day = (1/3)/20 = 1/60
=> A can complete the work in 60 days

A is thrice as good as B in work. A is able to finish a job in 60 days less than B. They can finish the work in___________days if they work together.

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A is thrice as good as B in work. A is able to finish a job in 60 days less than B. They can finish the work in___________days if they work together.

A. 18 days
B. 22 ½ days
C. 24 days
D. 26 days
If A completes a work in 1 day, B completes the same work in 3 days
Hence, if the difference is 2 days, B can complete the work in 3 days
=> if the difference is 60 days, B can complete the work in 90 days
=> Amount of work B can do in 1 day= 1/90
Amount of work A can do in 1 day = 3 × (1/90) = 1/30
Amount of work A and B can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45
=> A and B together can do the work in 45/2 days = 22 ½ days

Two taps X and Y can fill a tank in 10 hrs. and 15 hrs.respectively.  If the both taps are opened together, the tank will be full in_________?

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Two taps X and Y can fill a tank in 10 hrs. and 15 hrs.respectively.  If the both taps are opened together, the tank will be full in_________?

A. 3 hrs.
B. 4 hrs,
C. 5 hrs.
D. 6 hrs.
X’s 1 hour work = 1/10
Y’s 1 hour work = 1/15
(x+y)’s 1 hour work = 1/10+1/15=5/30=1/6
Both the taps can fill the tank in 6 hrs.

A, B and C together earn Rs.150 per day while A and C together earn Rs.94 and B and C together earn Rs.76. The daily earning of C is:__________?

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A, B and C together earn Rs.150 per day while A and C together earn Rs.94 and B and C together earn Rs.76. The daily earning of C is:__________?

A. 10 Rs,
B. 15 Rs,
C. 20 Rs.
D. 25 Rs.
B’s daily earning = Rs.(150-94)= Rs.56
A’s daily earning = Rs.(150-76)= Rs.74
C’s daily earning = Rs.[(150-(56+74)]=Rs.20