Question

The smallest number which when divided
by 20, 25, 35 and 40 leaves a remainder of
14, 19, 29 and 34 respectively, is
(A) 1394
(B) 1404
(C) 1664
(D) 1406
please help me to solve this question​

Answer 1

(1) Find the LCM:

20 = 2 * 2 * 5

25 = 5 * 5

35 = 5 * 7

40 = 2 * 2 * 2 * 5

LCM = 2 * 2 * 2 * 5 * 5 * 7

        = 1400

(2) Difference:

20 - 14 = 6

25 - 19 = 6

35 - 29 = 6

40 - 34 = 6

Here, difference between number and remainder is same in each case.

(iii)

Hence, the required number:

= 1400 - 6

= 1394

Hope it helps!