Question

A sum of 1,710 is divided in A, B
and C such that 4 times of A, 6 times
of B and 9 times of C are equal. What
is the difference between A and C ?
(1) 8360
(2) 450
(3) 480
(4) 540​

Answer 1

Answer:

2) 450

Step-by-step explanation:

A+B+C = 1710 ..................(1)

4A = 6B = 9C ..................(2)

from (1) A+B+C = 1710

A = 1710-B-C ............(3)

now from (2)

4A = 6B

2A = 3B (dividing both sides by 2)

putting the value of (3) we get,

2( 1710-B-C ) = 3B

3420-2B-2C = 3B

3420-2C = 5B

B = 3420/5 -2C/5

B = 684 - 2C/5 ............(4)

again from (2)

6B = 9C

B = 9C/6

B = 3C/2

putting the value of (4) in B we get

684 - 2C/5 = 3C/2

3C/2 + 2C/5 = 684

19C/10 = 684

19C = 6840

C = 360 ..............(5)

now putting the value of (5) in (4) we get

B = 684 -2(360)/5

B = 684 - 720/5

B = 684 - 144

B = 540 .............(6)

now put the value of (5) & (6) in (1)

A+540+360=1710

A = 1710 - 900

A = 810

Hence the difference between A and C is

A - C = 810 - 360 = 450

Answer 2

Answer:

The difference between A and C is 450.

Let, A + B + C = 1710 ........... (1)

Now, given that 4 times of A, 6 times of B and 9 times of C are equal.

So, 4A = 6B = 9C = K say.

So, A =k/4 , B =  k/6 and C = k/9

Hence, from equation (1) we get.

k/4 + k/6+ k/9=1710

k(9+6+4)/36=1710

19k/36=1710

K = 3240

Hence, A = k/4 = 810

B = k/6 = 540 and

C =k/9  = 360

Therefore, the difference between A and C is (810 - 360)=450