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Q.

Three tankers contain 403 liters , 434 liters and 465 liters of diesel respectively. Find the maximum capacity of the container that can measure the diesel of the three containers the exact number of times.

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a

31

b

12

c

15

d

20

answer is A.

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Detailed Solution

Concept- we will take the HCF of three tankers to find the maximum capacity out of the HCF of 403,434,465, find the common factor in all 3 HCF .Compare them to find maximum capacity .We will find HCF by prime factorization method.
Amount of diesel present in the first tank

= 403 liters

Amount of diesel present in second tank

= 434 liters

Amount of diesel poresent in third tank

= 465 liters

Maximum capacity

= HCF (403, 434, 465)

We will find HCF by prime factorization.
Prime factorization of 403,434,465.

403 = 1 \times 13 \times 31

434 = 1 \times 2 \times 7 \times 31

465 = 1 \times 3 \times 5 \times 31

Now,

HCF 403, 434, 465 = 31

So, here we got the maximum measuring capacity as 31 liters.
Hence, the correct answer is option 1.

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