CUET UG 2024 — General Test Quantitative Reasoning

Let the HCF be $h$h. Then the LCM is $60h$60h.

According to the problem, we have:

$$h + 60h = 854$$h+60h=854

This simplifies to:

$$61h = 854$$61h=854

Thus,

$h = \frac{854}{61} = 14$h=61854​=14.

Now, the LCM is:

$LCM = 60h = 60 \times 14 = 840$LCM=60h=60×14=840.

Using the relationship between LCM, HCF, and the two numbers, we have:

$LCM = \frac{a \times b}{HCF}$LCM=HCFa×b​,

where $a = 70$a=70 and $b$b is the unknown number.

Substituting the known values:

$840 = \frac{70 \times b}{14}$840=1470×b​.

This simplifies to:

$840 = 5b$840=5b.

Thus,

$b = \frac{840}{5} = 168$b=5840​=168.

The other number is 168.