CUET UG 2025 — General Test Arithmetic

When an amount is placed at compound interest and becomes double in 5 years, the time required for it to become eight times can be found using the doubling pattern.

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In compound interest, the amount grows by multiplication. Since the amount doubles in 5 years:

After 5 years: Amount $= 2 \times$=2× original

After 10 years: Amount $= 2 \times 2 = 4 \times$=2×2=4× original

After 15 years: Amount $= 4 \times 2 = 8 \times$=4×2=8× original

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Using the compound interest formula $A = P(1 + r)^t$A=P(1+r)t

Since the amount doubles in 5 years:

$$2 = (1 + r)^5$$2=(1+r)5

For the amount to become 8 times:

$$8 = (1 + r)^t$$8=(1+r)t

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Since $8 = 2^3$8=23:

$$8 = 2^3$$8=23

$$8 = [(1 + r)^5]^3$$8=[(1+r)5]3

$$8 = (1 + r)^{15}$$8=(1+r)15

Therefore $t = 15$t=15 years

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The amount will become eight times in 15 years.

When money doubles in $n$n years, it becomes $2^k$2k times in $k \times n$k×n years. Here, $8 = 2^3$8=23 and $n = 5$n=5, so the time required is $3 \times 5 = 15$3×5=15 years.