If x, y, z are positive integers such that x:y = 1:2 and y:z = 3:5, then which one of the following will be possible value of 5x-3y+z?

Start by making y the same in both ratios. x:y = 1:2 gives y = 2a, x = a. y:z = 3:5 gives y = 3b, z = 5b. The common value of y is the LCM of 2 and 3, which is 6. So y = 6t, x = 3t, z = 10t for some positive integer t. Check: x:y = 3t:6t = 1:2 and y:z = 6t:10t = 3:5.

Now substitute: 5x - 3y + z = 15t - 18t + 10t = 7t. The value must be a multiple of 7.

• A) 180 is wrong, since 180 is not divisible by 7 (7 x 25 = 175).
• B) 190 is wrong, since 190 leaves remainder 1 on division by 7.
• C) 196 is correct, since 196 = 7 x 28, giving t = 28.
• D) 200 is wrong, since 200 leaves remainder 4 on division by 7.

The core concept is combining ratios through a common term and then reading the result as a multiple of the common factor. This kind of chained-ratio reasoning is also what you need for proportion-based data questions in Mains.

Trap: aspirants often take y = 2 and y = 3 separately and never align y, which produces a wrong ratio for x, y, z. Always bring the shared term to a common value first.