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The World of Numbers: CBSE Class 9 Mathematics practice questions

Practise 50 questions on The World of Numbers, free, with an explanation for each answer.

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Sample questions

At the port of Lothal, a merchant gets 15 copper ingots for every 2 bags of spices. He brings 12 bags of spices. How many ingots does he take back?

Bags of spices and a stack of copper ingots on a dock at an ancient port, with a boat on the sea
  1. 180
  2. 90
  3. 27
  4. 1.6
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B. 90

12 bags make 12÷2=612 \div 2 = 6 lots of 2 bags, and each lot earns 15 ingots: 6×15=906 \times 15 = \mathbf{90} ingots. Taking 15×12=18015 \times 12 = 180 forgets that 15 ingots are paid for 2 bags, not 1. Adding 15+12=2715 + 12 = 27 makes no sense for a rate, and 12×215=1.612 \times \dfrac{2}{15} = 1.6 turns the ratio upside down.

One column of the Ishango bone has groups of 11, 13, 17 and 19 notches. If the carver had continued the same pattern, which three groups would come next?

A carved bone with four groups of tally notches labelled 11, 13, 17 and 19
  1. 23, 29, 31
  2. 21, 23, 25
  3. 23, 29, 37
  4. 23, 27, 29
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A. 23, 29, 31

11, 13, 17 and 19 are exactly the prime numbers between 10 and 20 (15 is skipped because 15=3×515 = 3 \times 5). The next primes are 23, 29 and 31. "21, 23, 25" just lists odd numbers, but 21=3×721 = 3 \times 7 and 25=5225 = 5^2. "23, 27, 29" wrongly counts 27=3327 = 3^3 as prime, and "23, 29, 37" skips the prime 31.

Find the rational number xx such that 56(x+35)=56x+12\dfrac{5}{6}\left(x + \dfrac{3}{5}\right) = \dfrac{5}{6}x + \dfrac{1}{2}.

A level balance with an expression in each pan
  1. Only x=0x = 0
  2. No rational number works
  3. Only x=35x = \dfrac{3}{5}
  4. Every rational number xx works
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D. Every rational number xx works

By the distributive law, 56(x+35)=56x+56×35=56x+12\dfrac{5}{6}\left(x + \dfrac{3}{5}\right) = \dfrac{5}{6}x + \dfrac{5}{6} \times \dfrac{3}{5} = \dfrac{5}{6}x + \dfrac{1}{2}, which is exactly the right side. So the equation is an identity: every rational xx satisfies it. Checking only x=0x = 0 (or 35\dfrac{3}{5}) finds one solution but misses the rest. Saying "no solution" usually comes from forgetting to multiply 35\dfrac{3}{5} by 56\dfrac{5}{6} and comparing 35\dfrac{3}{5} with 12\dfrac{1}{2}.

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