Question 12 - CBSE Class 10 Sample Paper for 2027 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

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Question 12 The mean age of a combined group of men and women is 35 years. If the mean ages of the men and women are 38 years and 30 years respectively, then the percentage of women in the group is: (A) 15 (B) 25.5 (C) 35 (D) 37.5 Given that Combined Mean age of of men and women = 35 years Mean age of men = 38 years Mean ages of women = 30 years Let Number of men be x Number of women be y We find Combined Mean using the formula Combined Mean = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑒𝑛 × 𝑀𝑒𝑛^(′)𝑠 𝑚𝑒𝑎𝑛 + 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑜𝑚𝑒𝑛 × 𝑊𝑜𝑚𝑒𝑛^(′)𝑠 𝑚𝑒𝑎𝑛)/(𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑒𝑛 + 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑜𝑚𝑒𝑛) Putting values 𝟑𝟓=(𝒙 × 𝟑𝟖 + 𝒚 × 𝟑𝟎)/(𝒙 + 𝒚) 35=(38𝑥 + 30𝑦)/(𝑥 + 𝑦) Solving 𝟑𝟖𝒙 + 𝟑𝟎𝒚 =𝟑𝟓(𝒙+𝒚) 38𝑥 + 30𝑦 =35𝑥+35𝑦 38𝑥 −35𝑥 =35𝑦−30𝑦 3𝑥=5𝑦 𝒙=(𝟓𝒚)/(𝟑) We need to find percentage of women in the group Now, Percentage of women in the group = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑜𝑚𝑒𝑛)/(𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑒𝑛+𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑜𝑚𝑒𝑛) × 100 = (𝒚)/(𝒙 + 𝒚) × 𝟏𝟎𝟎 Putting 𝑥=(5𝑦)/(3) = (𝑦)/(((5𝑦)/(3)) + 𝑦) × 100 = (𝑦)/((5𝑦 + 3𝑦)/(3)) × 100 = (𝑦)/((8𝑦)/(3)) × 100 = (3𝑦)/(8𝑦) × 100 = (3)/(8) × 100 = 3 × 12.5 = 37.5% So, the correct answer is (D) Combined Mean = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑒𝑛 × 𝑀𝑒𝑛^(′)𝑠 𝑚𝑒𝑎𝑛 + 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑜𝑚𝑒𝑛 × 𝑊𝑜𝑚𝑒𝑛^(′)𝑠 𝑚𝑒𝑎𝑛)/(𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑒𝑛 + 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑜𝑚𝑒𝑛) Putting values 𝟑𝟓=(𝒙 × 𝟑𝟖 + 𝒚 × 𝟑𝟎)/(𝒙 + 𝒚) 35=(38𝑥 + 30𝑦)/(𝑥 + 𝑦) Solving 𝟑𝟖𝒙 + 𝟑𝟎𝒚 =𝟑𝟓(𝒙+𝒚) 38𝑥 + 30𝑦 =35𝑥+35𝑦 38𝑥 −35𝑥 =35𝑦−30𝑦 3𝑥=5𝑦 𝒙=(𝟓𝒚)/(𝟑) We need to find percentage of women in the group Now, Percentage of women in the group = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑜𝑚𝑒𝑛)/(𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑒𝑛+𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑜𝑚𝑒𝑛) × 100 = (𝒚)/(𝒙 + 𝒚) × 𝟏𝟎𝟎 Putting 𝑥=(5𝑦)/(3) = (𝑦)/(((5𝑦)/(3)) + 𝑦) × 100 = (𝑦)/((5𝑦 + 3𝑦)/(3)) × 100 = (𝑦)/((8𝑦)/(3)) × 100 = (3𝑦)/(8𝑦) × 100 = (3)/(8) × 100 = 3 × 12.5 = 37.5% So, the correct answer is (D) We need to find percentage of women in the group Now, Percentage of women in the group = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑜𝑚𝑒𝑛)/(𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑒𝑛+𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑜𝑚𝑒𝑛) × 100 = (𝒚)/(𝒙 + 𝒚) × 𝟏𝟎𝟎 Putting 𝑥=(5𝑦)/(3) = (𝑦)/(((5𝑦)/(3)) + 𝑦) × 100 = (𝑦)/((5𝑦 + 3𝑦)/(3)) × 100 = (𝑦)/((8𝑦)/(3)) × 100 = (3𝑦)/(8𝑦) × 100 = (3)/(8) × 100 = 3 × 12.5 = 37.5% So, the correct answer is (D) = (𝟑)/(𝟖) × 𝟏𝟎𝟎 = 3 × 12.5 = 37.5% So, the correct answer is (D)