A number is first decreased by one-fifth of its value and then increased by one-fourth of the resulting value. If the final result is 48, what was the original number ?
48
A decrease by one-fifth leaves four-fifths of the number, and an increase by one-fourth multiplies the value by five-fourths. Successive fractional changes are applied one after the other as multipliers.
Step 1 — Let the original number be \(x\). After decreasing it by one-fifth, the value becomes \(x - \frac{x}{5} = \frac{4x}{5}\).
Step 2 — Increasing this by one-fourth of itself gives \(\frac{4x}{5} \times \frac{5}{4} = x\). The two changes cancel exactly, so the final value equals the original number.
Step 3 — The final result is 48, therefore \(x = 48\).
Taking 46, 54 or 50 as the starting number would also return the same number at the end, i.e. 46, 54 or 50, not 48, so none of these fits.
48 option is correct.
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Important Questions from Fractions
Simplify the expression 441 ÷ \(\left[270 \div \frac{3}{7}+\left(17\div \frac{1}{3}\right)-\left(8\frac{1}{2}-\frac{5}{2}\right)\right]\)
Number 0.232323 can be written in rational form as:
Solve: \(\frac{1}{2}\) [{-2(2 + 3)*20}/2]
Match the following.
Column I
Column II
a.
Equivalent fraction of \(\frac{7}{12}\) is
i.
Proper fraction
b.
Equivalent fraction of \(\frac{9}{15}\) is
ii.
Improper fraction
c.
\(\frac{7}{11}\) is
iii.
\(\frac{21}{36}\)
d.
\(\frac{19}{5}\) is
iv.
\(\frac{3}{5}\)
Among the fractions \(\frac{7}{12}\) , \(\frac{8}{15}\) , \(\frac{17}{24}\) and \(\frac{13}{18}\) , which is the smallest?
