CUET UG 2025 — General Test Quantitative Reasoning

A number when divided by 95 leaves a remainder 43. The same number divided by 19 needs to be found.

If a number gives remainder 43 when divided by 95, it can be written as:

$$N = 95k + 43$$N=95k+43

where $k$k is the quotient.

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Breaking down 95 and 43 using 19:

$$95 = 19 \times 5$$95=19×5

$$43 = 19 \times 2 + 5$$43=19×2+5

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Substituting into the equation:

$$N = 95k + 43$$N=95k+43

$$N = (19 \times 5)k + (19 \times 2 + 5)$$N=(19×5)k+(19×2+5)

$$N = 19 \times 5k + 19 \times 2 + 5$$N=19×5k+19×2+5

$$N = 19(5k + 2) + 5$$N=19(5k+2)+5

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The final form shows:

$$N = 19(5k + 2) + 5$$N=19(5k+2)+5

This means the number equals 19 times some integer, plus 5.

Therefore, when $N$N is divided by 19, the remainder is $5$5.