Chain Rule Challenge

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Directions: Each of the questions given below is followed by series of options among which you have to choose the best one. You can also review your choices by clicking into answer section.


1. If 15 toys cost Rs.234, what do 35 toys cost?

A. 486

B. 546

C. 626

D. 686


Answer

                  Ans: Option B

       Explanation:

       Let the required cost be Rs. x.

       Then, more toys, more cost (Direct Proportion)

       15 : 35 : : 234 : x

       (15 * x) = (35 * 234)

       x = (35 * 234)/15 = 546

       Hence, the cost of 35 toys is Rs.546. 


2. If the cost of x meters of wire is d rupees, then what is the cost of y metres of wire at the same rate?

A.  Rs.(xy/d)  

B. Rs.(xd)

C.Rs.(yd)

D. Rs.(yd/x) 


Answer

                  Ans: Option D

       Explanation:

       Cost of x metres = Rs. d.

       Cost of 1 metre = Rs.   d/x

       Cost of y metres = Rs. (d/x )y   = Rs.   yd/x 


3. Some persons can do a piece of work in 12 days. Two times the number of such persons will do half of that work in

A. 6 days

B. 12 days

C. 3 days

D. 4 days


Answer

                  Ans: Option C

       Explanation:

       Mens (2x : x) : (work 1:1/2) :: 12 :y

       2x*1* y = x*1/2 *12 or y = 3 


4. A man completes   of a job in 10 days. At this rate, how many more days will it takes him to finish the job?

A. 5

B. 6

C. 7

D. 8


Answer

                  Ans: Option B

       Explanation:

       Work done = 5/8

       Balance work =   1 – 5/8= 3/8

       Let the required number of days be x.

       Then, 5/8 : 3/8 = :: 10 : x      

       (5/8) * x = (3/8) * 10

        x =   (3/8) * 10 * (8/5)

        x = 6. 


5. The price of 357 mangoes is Rs. 1517.25. What will be the approximate price of 49 dozens of such mangoes?

A. Rs. 3000

B. Rs. 4000

C. Rs. 3500

D. Rs. 2500


Answer

                  Ans: Option D

       Explanation:

       More mangoes, more cost (Direct)

       357 : 49 * 12 :: 1517.25 : x

       or, 375*x= 49  12 * 1517.25.

       49*12*1517.25 / 357 = 2499

       Approximate cost = Rs. 2500. 


6. A rope can make 70 rounds of the circumference of a cylinder whose radius of the base is 14cm. how many times can it go round a cylinder having radius 20 cm?

A. 49 rounds

 B. 42 rounds

C. 54 rounds

 D. 52 rounds


Answer

                  Ans: Option A

       Explanation:

       Let the required number of rounds be x

       More radius, less rounds (Indirect proportion)

       Hence we can write as

       Radius 14:20 :: x:70

       14×70=20x

       14×7=2x

       x=7×7=49 


7. A person works on a project and completes 5/8 of the job in 10 days. At this rate, how many more days will he it take to finish the job?

A. 7

B. 6

C. 5

D. 4


Answer

                  Ans: Option B

       Explanation:

       Number of days he worked = 10

       Work completed = 5/8

       Let the required number of days = x

       Remaining Work to be completed = 1 – 5/8 = 3/8

       More work, more days(direct proportion)

       Hence we can write as

       Work 5/8:3/8}:: 10:x

       5/8x=3/8×10

       5x=3×10

       x=3×2=6 


8. If 12 carpenters, working.6 hours a day can make 460 chairs in 24 days, how many chairs will 18 carpenters make in 36 days, each working 8hours a day?

A. 1260

B. 920

C. 1320

D. 1380


Answer

                  Ans: Option D

       Explanation:

       (Carpenters 12: 18) : (His/Day 6:8 ) : (Days 24 : 36) : : 460 : x

       12*6* 24*x =18*8*36*460

       Or, x = 1380 


9. In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?

A.1

B.1/40

C.40

D. 80


Answer

                  Ans: Option C

       Explanation:

       Let the required number of days be x.

       Less cows, more days (Indirect Proportion)

       Less bags, less days (Direct Proportion)

       Cows 1 : 40  

       :: 40 : x

       Bags  40 : 1 

       1 x 40 x x = 40 x 1 x 40

        x = 40. 


10. 14 pumps of equal capacity can fill a tank in 6 days. If the tank has to be filled in 4 days, the number of extra pumps needed is.

A. 7

B. 21

C. 14

D. 28


Answer

                  Ans: Option A

       Explanation:

       4 : 6 :: 14 : x

       or, 4x =6 * 14

       or, x = 6*14/4 = 21

       Extra pumps needed = (21 – 14) = 7. 


11. If 18 persons can build a wall 140 m long in 42 days, the number of days that 30 persons will take to complete a similar wall 100 m long, is.

A. 18

B. 24

C. 21

D. 28


Answer

                  Ans: Option A

       Explanation:

       Length (140:100): (Persons 30:18) :: 42 : x

       140*30*x = 100*18*42

       Or, x = 18 


12. If 80 lamps can be lighted 5 hours per day for 10 days for Rs. 21.25,then the number of lamps which can be lighted 4 hours daily for 30days for Rs. 76.50, is :

A. 100

B. 150

C. 120

D. 160


Answer

                  Ans: Option C

       Explanation:

       (Hrs/Day 4: 5): (Money 21.25 :76.50) : (Days 30:10) : : 80 : x

       4*21.25*30*x = 5*76.50*10*80

       So, x = 120 


13. On a scale of a map 0.6 cm represents 6.6km. If the distance between two points on the map is 80.5 cm , what is the actual distance between these points?

A. 885.5 km

B. 860 km

C. 892.5 km

D. 825 km


Answer

                  Ans: Option A

       Explanation:

       Let the required actual distance be x km

       More scale distance, More actual distance (direct proportion)

       Hence we can write as

       Scale distance.6:80.5}::6.6:x

       ⇒.6x=80.5×6.6⇒.1x=80.5×1.1⇒x=80.5×11=885.5 


14. A wheel rotates 10 times every minute and moves 20 cm during each rotation. How many cms does the wheel move in 1 hour?

A. 2000

B. 1200

C. 600

D. 12000


Answer

                  Ans: Option D

       Explanation:

       Number of wheel moves in 1 hour = 10 * 60 = 600

       Distance moved = 600 * 20 = 12000 


15. 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?

 A.4

 B.8

C.12

D.16


Answer

                  Ans: Option D

       Explanation:

       Let the required number of bottles be x.

       More weavers, more mats (Direct Proportion)

       More days, more mats (Direct Proportion)

       Wavers 4 : 8   :: 4 : x

       Days 4 : 8 

       4 x 4 x x = 8 x 8 x 4

       x = (8 x 8 x 4)

       (4 x 4)

        x = 16. 


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