question_answer 1)

Find the whole quantity  if (a) 5% of it is 600.                                                             (b) 12% of it is ` 1080 (c) 40% of it is 500 km.                                                    (d) 70% of it is 14 minutes. (e) 8% of it is 40 litres.                

Answer:

                (a) Let the whole quantity be P. Then,                 5% of P = 600                 \[\Rightarrow \]               \[\frac{5}{100}\times P=600\] \[\Rightarrow \]               \[\frac{P}{20}=600\] \[\Rightarrow \]               \[P=600\times 20\] \[\Rightarrow \]               \[P=12000\] Hence, the whole quantity is 12000. (b) Let the whole quantity ` P. Then,                   12% of P = 1080. \[\Rightarrow \]               \[\frac{12}{100}\times P=\] ` 1080 \[\Rightarrow \]               \[\frac{3P}{25}=\] ` 1080 \[\Rightarrow \]               \[P=\frac{1080\times 25}{3}\] \[\Rightarrow \]               P = ` 9000 Hence, the whole quantity is ` 9000 (c) Let the whole quantity be P km. Then,                 40% of P = 500 \[\Rightarrow \]               \[\frac{40}{100}\times P=500\] \[\Rightarrow \]               \[\frac{2P}{5}=500\] \[\Rightarrow \]               \[P=\frac{500\times 5}{2}\] \[\Rightarrow \]               \[P=125\text{0 km}\]. Hence, the whole quantity is 1250 km. (d) Let the whole quantity be P minutes Then, 70% of P = 14                 \[\Rightarrow \]               \[\frac{70}{100}\times P=14\]                 \[\Rightarrow \]               \[\frac{7P}{10}=14\]                 \[\Rightarrow \]               \[P=\frac{14\times 10}{7}\]                 \[\Rightarrow \]               P = 20                 Hence, the whole quantity is 20 minutes.                 (e) Let the whole quantity be P litres. Then.                                 8% of P = 40                 \[\Rightarrow \]               \[\frac{8}{100}\times P=40\]                 \[\Rightarrow \]               \[\frac{2P}{25}=40\]                 \[\Rightarrow \]               \[P=\frac{40\times 25}{2}\]                 \[\Rightarrow \]               \[P=500\]                 Hence, the whole quantity is 500 litres.