Example 6 (Page 10) - Chapter 1 Class 8 - Fractions in Disguise (Ganita Prakash II)

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Example 6 (Page 10) Kishanlal recently opened a garment shop. He aims to achieve a daily sales of at least ₹5000. The sales on the first 2 days were ₹2000 and ₹3500. What percentage of his target did he achieve? In the next two days, he made ₹5000 and ₹6000 respectively. What percentage of his target are these values? What percentage of the target was achieved on Day 4? On Days 5 and 6 his sales were ₹7800 and ₹9550 respectively. Calculate the percentage of the target achieved on these days. On Day 7, he achieved 150% of his target. On Day 8, he achieved 210% of his target. Find the sales made on these days. Let’s answer this one-by-one Given that Kishanlal aims to achieve a daily sales of at least ₹5000. The sales on the first 2 days were ₹2000 and ₹3500. Making a bar Diagram For Day 1 Calculating Percentage of Target % of Target = 𝐴𝑚𝑜𝑢𝑛𝑡/(𝑇𝑜𝑡𝑎𝑙 𝑎𝑚𝑜𝑢𝑛𝑡) × 100 = 𝟐𝟎𝟎𝟎/𝟓𝟎𝟎𝟎 × 𝟏𝟎𝟎 = 2/5 × 100 = 2 × 20 = 40% For Day 2 Calculating Percentage of Target % of Target = 𝐴𝑚𝑜𝑢𝑛𝑡/(𝑇𝑜𝑡𝑎𝑙 𝑎𝑚𝑜𝑢𝑛𝑡) × 100 = 𝟑𝟓𝟎𝟎/𝟓𝟎𝟎𝟎 × 𝟏𝟎𝟎 = 35/50 × 100 = 7/10 × 100 = 7 × 10 = 70% Thus, it is 40% on Day 1 and 70% on Day 2 Another way of saying it is — he was 60% short of his target on Day 1 and 30% short of his target on Day 2. Now, the next part of our question is In the next two days, he made ₹5000 and ₹6000 respectively. What percentage of his target are these values? For Day 3 He made ₹ 5000, and his target was ₹ 5000, so that means he achieved 100% of the target For Day 4 He made ₹ 6000, and target was ₹ 5000. This means he exceeded his target – let’s find how much percentage of target he is on now % of Target = 𝐴𝑚𝑜𝑢𝑛𝑡/(𝑇𝑜𝑡𝑎𝑙 𝑎𝑚𝑜𝑢𝑛𝑡) × 100 = 𝟔𝟎𝟎𝟎/𝟓𝟎𝟎𝟎 × 𝟏𝟎𝟎 = 6/5 × 100 = 6 × 20 = 120% Thus on Day 4, he achieved 120% of his target, i.e., 20% more than his target Now, the next part of our question is On Days 5 and 6 his sales were ₹7800 and ₹9550 respectively. Calculate the percentage of the target achieved on these days. For Day 5 He made ₹ 7800, and target was ₹ 5000. Calculating percentage of target % of Target = 𝐴𝑚𝑜𝑢𝑛𝑡/(𝑇𝑜𝑡𝑎𝑙 𝑎𝑚𝑜𝑢𝑛𝑡) × 100 = 𝟕𝟖𝟎𝟎/𝟓𝟎𝟎𝟎 × 𝟏𝟎𝟎 = 78/50 × 100 = 78 × 2 = 156% For Day 6 He made ₹ 7800, and target was ₹ 9550. Calculating percentage of target % of Target = 𝐴𝑚𝑜𝑢𝑛𝑡/(𝑇𝑜𝑡𝑎𝑙 𝑎𝑚𝑜𝑢𝑛𝑡) × 100 = 𝟗𝟓𝟓𝟎/𝟓𝟎𝟎𝟎 × 𝟏𝟎𝟎 = 955/500 × 100 = 955/5 = 191% Finally, the last part of our question is On Day 7, he achieved 150% of his target. On Day 8, he achieved 210% of his target. Find the sales made on these days For Day 7 Since his target was ₹ 5000, and he achieved 150% of it Thus, we can write Sales made on Day 7 = 150% × ₹ 5000 = 𝟏𝟓𝟎/𝟏𝟎𝟎 × 𝟓𝟎𝟎𝟎 = 15/10 × 5000 = 15 × 500 = ₹ 7500 Thus, his sales was ₹ 7500 For Day 8 Since his target was ₹ 5000, and he achieved 210% of it Thus, we can write Sales made on Day 7 = 210% × ₹ 5000 = 𝟐𝟏𝟎/𝟏𝟎𝟎 × 𝟓𝟎𝟎𝟎 = 21/10 × 5000 = 21 × 500 = ₹ 10,500 Thus, his sales was ₹ 10,500 Thus on Day 4, he achieved 120% of his target, i.e., 20% more than his target Now, the next part of our question is On Days 5 and 6 his sales were ₹7800 and ₹9550 respectively. Calculate the percentage of the target achieved on these days. For Day 5 He made ₹ 7800, and target was ₹ 5000. Calculating percentage of target % of Target = 𝐴𝑚𝑜𝑢𝑛𝑡/(𝑇𝑜𝑡𝑎𝑙 𝑎𝑚𝑜𝑢𝑛𝑡) × 100 = 𝟕𝟖𝟎𝟎/𝟓𝟎𝟎𝟎 × 𝟏𝟎𝟎 = 78/50 × 100 = 78 × 2 = 156% For Day 6 He made ₹ 7800, and target was ₹ 9550. Calculating percentage of target % of Target = 𝐴𝑚𝑜𝑢𝑛𝑡/(𝑇𝑜𝑡𝑎𝑙 𝑎𝑚𝑜𝑢𝑛𝑡) × 100 = 𝟗𝟓𝟓𝟎/𝟓𝟎𝟎𝟎 × 𝟏𝟎𝟎 = 955/500 × 100 = 955/5 = 191% Finally, the last part of our question is On Day 7, he achieved 150% of his target. On Day 8, he achieved 210% of his target. Find the sales made on these days For Day 7 Since his target was ₹ 5000, and he achieved 150% of it Thus, we can write Sales made on Day 7 = 150% × ₹ 5000 = 𝟏𝟓𝟎/𝟏𝟎𝟎 × 𝟓𝟎𝟎𝟎 = 15/10 × 5000 = 15 × 500 = ₹ 7500 Thus, his sales was ₹ 7500 For Day 8 Since his target was ₹ 5000, and he achieved 210% of it Thus, we can write Sales made on Day 7 = 210% × ₹ 5000 = 𝟐𝟏𝟎/𝟏𝟎𝟎 × 𝟓𝟎𝟎𝟎 = 21/10 × 5000 = 21 × 500 = ₹ 10,500 Thus, his sales was ₹ 10,500