Ex 5.2 Q20 - Ramkali saved ₹5 in the first week of a year and then increased her weekly savings by ₹1.75. If in the nth week, her weekly savings become ₹20.75, find n.
Solution:- Ramkali saved ₹5 in the first week and then increased her weekly savings by ₹1.75,
∴ Saving in 1st week = ₹5
∴ Saving in 2nd week
= ₹(5 + 1.75)
= ₹6.75
∴ Saving in 3rd week
= ₹(6.75 + 1.75)
= ₹8.50
*So weekly saving by Ramkali is..
5, 6.75, 8.50...
*Clearly this forms an AP with
a = 5 d = 1.75
➙ In nth week, her weekly savings become ₹20.75,
∴ aₙ = 20.75
*Using formula, aₙ = a + (n - 1)d
∴ a + (n - 1)d = 20.75
∴ 5 + (n - 1)1.75 = 20.75
∴ 5 + 1.75n - 1.75 = 20.75
∴ 1.75n = 20.75 + 1.75 - 5
∴ 1.75n = 17.5
∴ n =
17.5
/
1.75
∴ n = 10
Hence,
In 10th week, Ramkali's weekly savings become ₹20.75.
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Try This..
✒ A student saves ₹8 in the first week and increases her saving by ₹1.50 each week. What will be her savings in the 15th week?
✒ Ravi saved ₹4 in the first week and increased his saving by ₹2 every week. How much will he save in the 12th week?
✒ The savings in the 1st week is ₹3.75 and increases by ₹2.25 each week. In which week will the savings be ₹28.50?
✒ The weekly savings of a student form an AP. If the 5th week’s saving is ₹14 and the 9th week’s saving is ₹22, find the first term and common difference.
❌ Common Mistakes
Mixing Total Saving with Weekly Saving:▸ The question is about weekly saving, not the total amount saved till that week.Wrong Formula Application:▸ Remember to use an = a + (n – 1)d; not the sum formula!Calculation Errors in Division:▸ Dividing decimals like 17.5 ÷ 1.75? Use a calculator or long division carefully.Ignoring Units:▸ Don’t forget we’re dealing with rupees. Keep the currency consistent in the answer.
📝 Related Questions:-
Queries Solved:-
Class 10 Ex 5.2
Ex 5.2 Q20 Class 10
Class 10 Ex 5.2 Q20
Class 10 Chap 5 Ex 5.2 Q20
Class 10 Arithmetic Progression
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